diff --git a/CHANGELOG.md b/CHANGELOG.md
index dc21fb6422c..e591e565a04 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -17,6 +17,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Add FFI definition `PyFrame_GetCode`. [#2406](https://github.com/PyO3/pyo3/pull/2406)
 - Added `PyCode` and `PyFrame` high level objects. [#2408](https://github.com/PyO3/pyo3/pull/2408)
 - Add FFI definitions `Py_fstring_input`, `sendfunc`, and `_PyErr_StackItem`. [#2423](https://github.com/PyO3/pyo3/pull/2423)
+- Add `PyDateTime::new_with_fold`, `PyTime::new_with_fold`, `PyTime::get_fold`, `PyDateTime::get_fold` for PyPy. [#2428](https://github.com/PyO3/pyo3/pull/2428)
 
 ### Changed
 
@@ -39,7 +40,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Correct FFI definition `Py_tracefunc` to be `unsafe extern "C" fn` (was previously safe). [#2407](https://github.com/PyO3/pyo3/pull/2407)
 - Fix case where `ValueError` without message could be raised by the `#[derive(FromPyObject)]` generated implementation for a tuple struct. [#2414](https://github.com/PyO3/pyo3/pull/2414)
 - Fix compile failure when using `#[pyo3(from_py_with = "pouf")]` in on a field in a `#[derive(FromPyObject)]` struct. [#2414](https://github.com/PyO3/pyo3/pull/2414)
-- Fix FFI definitions `_PyDateTime_BaseTime` lacking leading underscores in their names. [#2421](https://github.com/PyO3/pyo3/pull/2421)
+- Fix FFI definitions `_PyDateTime_BaseTime` and `_PyDateTime_BaseDateTime` lacking leading underscores in their names. [#2421](https://github.com/PyO3/pyo3/pull/2421)
 - Remove FFI definition `PyArena` on Python 3.10 and up. [#2421](https://github.com/PyO3/pyo3/pull/2421)
 - Fix FFI definition `PyCompilerFlags` missing member `cf_feature_version` on Python 3.8 and up. [#2423](https://github.com/PyO3/pyo3/pull/2423)
 - Fix FFI definition `PyAsyncMethods` missing member `am_send` on Python 3.10 and up. [#2423](https://github.com/PyO3/pyo3/pull/2423)
@@ -47,6 +48,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fix FFI definition `PySyntaxErrorObject` missing members `end_lineno` and `end_offset` on Python 3.10 and up. [#2423](https://github.com/PyO3/pyo3/pull/2423)
 - Fix FFI definition `PyHeapTypeObject` missing member `ht_module` on Python 3.9 and up. [#2423](https://github.com/PyO3/pyo3/pull/2423)
 - Fix FFI definition `PyFrameObject` having multiple incorrect members on various Python versions. [#2424](https://github.com/PyO3/pyo3/pull/2424)
+- Fix FFI definition `PyTypeObject` missing deprecated field `tp_print` on Python 3.8. [#2428](https://github.com/PyO3/pyo3/pull/2428)
+- Fix FFI definitions `PyDateTime_CAPI`. `PyDateTime_Date`, `PyASCIIObject`, `PyBaseExceptionObject`, `PyListObject`, and `PyTypeObject` on PyPy. [#2428](https://github.com/PyO3/pyo3/pull/2428)
 
 ## [0.16.5] - 2022-05-15
 
diff --git a/pyo3-ffi/src/cpython/code.rs b/pyo3-ffi/src/cpython/code.rs
index 760afb7149d..894e61c231d 100644
--- a/pyo3-ffi/src/cpython/code.rs
+++ b/pyo3-ffi/src/cpython/code.rs
@@ -1,14 +1,17 @@
 use crate::object::*;
 use crate::pyport::Py_ssize_t;
-use std::os::raw::{c_char, c_int, c_uchar, c_void};
+#[cfg(not(PyPy))]
+use std::os::raw::c_uchar;
+use std::os::raw::{c_char, c_int, c_void};
 
 // skipped _Py_CODEUNIT
 // skipped _Py_OPCODE
 // skipped _Py_OPARG
 
-#[cfg(Py_3_8)]
+#[cfg(all(Py_3_8, not(PyPy)))]
 opaque_struct!(_PyOpcache);
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct PyCodeObject {
@@ -44,6 +47,9 @@ pub struct PyCodeObject {
     pub co_opcache_size: c_uchar,
 }
 
+#[cfg(PyPy)]
+opaque_struct!(PyCodeObject);
+
 /* Masks for co_flags */
 pub const CO_OPTIMIZED: c_int = 0x0001;
 pub const CO_NEWLOCALS: c_int = 0x0002;
diff --git a/pyo3-ffi/src/cpython/compile.rs b/pyo3-ffi/src/cpython/compile.rs
index f7aa7f8f37b..9a2afdb93e3 100644
--- a/pyo3-ffi/src/cpython/compile.rs
+++ b/pyo3-ffi/src/cpython/compile.rs
@@ -1,12 +1,12 @@
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 use crate::object::PyObject;
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 use crate::pyarena::*;
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 use crate::pythonrun::*;
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 use crate::PyCodeObject;
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 use std::os::raw::c_char;
 use std::os::raw::c_int;
 
@@ -30,6 +30,7 @@ pub struct PyCompilerFlags {
 
 // skipped non-limited _PyCompilerFlags_INIT
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct PyFutureFeatures {
@@ -49,10 +50,10 @@ pub const FUTURE_GENERATOR_STOP: &str = "generator_stop";
 // skipped non-limited FUTURE_ANNOTATIONS
 
 extern "C" {
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyNode_Compile(arg1: *mut _node, arg2: *const c_char) -> *mut PyCodeObject;
 
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyAST_CompileEx(
         _mod: *mut _mod,
         filename: *const c_char,
@@ -61,7 +62,7 @@ extern "C" {
         arena: *mut PyArena,
     ) -> *mut PyCodeObject;
 
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyAST_CompileObject(
         _mod: *mut _mod,
         filename: *mut PyObject,
@@ -70,10 +71,10 @@ extern "C" {
         arena: *mut PyArena,
     ) -> *mut PyCodeObject;
 
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyFuture_FromAST(_mod: *mut _mod, filename: *const c_char) -> *mut PyFutureFeatures;
 
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyFuture_FromASTObject(
         _mod: *mut _mod,
         filename: *mut PyObject,
diff --git a/pyo3-ffi/src/cpython/frameobject.rs b/pyo3-ffi/src/cpython/frameobject.rs
index 57037b17ea1..a8446244db6 100644
--- a/pyo3-ffi/src/cpython/frameobject.rs
+++ b/pyo3-ffi/src/cpython/frameobject.rs
@@ -1,14 +1,16 @@
 use crate::cpython::code::PyCodeObject;
 use crate::object::*;
 use crate::pystate::PyThreadState;
-use std::os::raw::{c_char, c_int};
-
-// skipped _framestate
+#[cfg(not(any(PyPy, Py_3_11)))]
+use std::os::raw::c_char;
+use std::os::raw::c_int;
 
+#[cfg(not(any(PyPy, Py_3_11)))]
 pub type PyFrameState = c_char;
 
 #[repr(C)]
 #[derive(Copy, Clone)]
+#[cfg(not(any(PyPy, Py_3_11)))]
 pub struct PyTryBlock {
     pub b_type: c_int,
     pub b_handler: c_int,
@@ -17,7 +19,7 @@ pub struct PyTryBlock {
 
 #[repr(C)]
 #[derive(Copy, Clone)]
-#[cfg(not(Py_3_11))]
+#[cfg(not(any(PyPy, Py_3_11)))]
 pub struct PyFrameObject {
     pub ob_base: PyVarObject,
     pub f_back: *mut PyFrameObject,
@@ -46,7 +48,7 @@ pub struct PyFrameObject {
     pub f_localsplus: [*mut PyObject; 1],
 }
 
-#[cfg(Py_3_11)]
+#[cfg(any(PyPy, Py_3_11))]
 opaque_struct!(PyFrameObject);
 
 // skipped _PyFrame_IsRunnable
@@ -74,6 +76,7 @@ extern "C" {
     // skipped _PyFrame_New_NoTrack
 
     pub fn PyFrame_BlockSetup(f: *mut PyFrameObject, _type: c_int, handler: c_int, level: c_int);
+    #[cfg(not(any(PyPy, Py_3_11)))]
     pub fn PyFrame_BlockPop(f: *mut PyFrameObject) -> *mut PyTryBlock;
 
     pub fn PyFrame_LocalsToFast(f: *mut PyFrameObject, clear: c_int);
diff --git a/pyo3-ffi/src/cpython/genobject.rs b/pyo3-ffi/src/cpython/genobject.rs
index a9807118ed5..88895a4846e 100644
--- a/pyo3-ffi/src/cpython/genobject.rs
+++ b/pyo3-ffi/src/cpython/genobject.rs
@@ -1,8 +1,10 @@
 use crate::object::*;
-use crate::pyport::Py_ssize_t;
-use crate::{PyFrameObject, _PyErr_StackItem};
+use crate::PyFrameObject;
+#[cfg(not(PyPy))]
+use crate::{Py_ssize_t, _PyErr_StackItem};
 use std::os::raw::c_int;
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct PyGenObject {
@@ -44,7 +46,7 @@ extern "C" {
     // skipped _PyGen_FetchStopIterationValue
     // skipped _PyGen_yf
     // skipped _PyGen_Finalize
-    #[cfg(not(Py_3_9))]
+    #[cfg(not(any(Py_3_9, PyPy)))]
     #[deprecated(note = "This function was never documented in the Python API.")]
     pub fn PyGen_NeedsFinalizing(op: *mut PyGenObject) -> c_int;
 }
diff --git a/pyo3-ffi/src/cpython/import.rs b/pyo3-ffi/src/cpython/import.rs
index d85eb5fadca..de58935a7ad 100644
--- a/pyo3-ffi/src/cpython/import.rs
+++ b/pyo3-ffi/src/cpython/import.rs
@@ -1,5 +1,7 @@
 use crate::{PyInterpreterState, PyObject};
-use std::os::raw::{c_char, c_int, c_uchar};
+#[cfg(not(PyPy))]
+use std::os::raw::c_uchar;
+use std::os::raw::{c_char, c_int};
 
 // skipped PyInit__imp
 
@@ -27,6 +29,7 @@ extern "C" {
     ) -> c_int;
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct _inittab {
@@ -36,13 +39,16 @@ pub struct _inittab {
 
 #[cfg_attr(windows, link(name = "pythonXY"))]
 extern "C" {
+    #[cfg(not(PyPy))]
     pub static mut PyImport_Inittab: *mut _inittab;
 }
 
 extern "C" {
+    #[cfg(not(PyPy))]
     pub fn PyImport_ExtendInittab(newtab: *mut _inittab) -> c_int;
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct _frozen {
@@ -53,5 +59,6 @@ pub struct _frozen {
 
 #[cfg_attr(windows, link(name = "pythonXY"))]
 extern "C" {
+    #[cfg(not(PyPy))]
     pub static mut PyImport_FrozenModules: *const _frozen;
 }
diff --git a/pyo3-ffi/src/cpython/listobject.rs b/pyo3-ffi/src/cpython/listobject.rs
index 13b82ff1dfb..012221da4fd 100644
--- a/pyo3-ffi/src/cpython/listobject.rs
+++ b/pyo3-ffi/src/cpython/listobject.rs
@@ -1,6 +1,8 @@
 use crate::object::*;
+#[cfg(not(PyPy))]
 use crate::pyport::Py_ssize_t;
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct PyListObject {
@@ -9,6 +11,11 @@ pub struct PyListObject {
     pub allocated: Py_ssize_t,
 }
 
+#[cfg(PyPy)]
+pub struct PyListObject {
+    pub ob_base: PyObject,
+}
+
 // skipped _PyList_Extend
 // skipped _PyList_DebugMallocStats
 // skipped _PyList_CAST (used inline below)
diff --git a/pyo3-ffi/src/cpython/object.rs b/pyo3-ffi/src/cpython/object.rs
index 86865245739..97baa9af3ca 100644
--- a/pyo3-ffi/src/cpython/object.rs
+++ b/pyo3-ffi/src/cpython/object.rs
@@ -276,6 +276,8 @@ pub struct PyTypeObject {
     pub tp_finalize: Option<object::destructor>,
     #[cfg(Py_3_8)]
     pub tp_vectorcall: Option<super::vectorcallfunc>,
+    #[cfg(all(Py_3_8, not(Py_3_9)))]
+    pub tp_print: Option<printfunc>,
     #[cfg(PyPy)]
     pub tp_pypy_flags: std::os::raw::c_long,
     #[cfg(py_sys_config = "COUNT_ALLOCS")]
diff --git a/pyo3-ffi/src/cpython/pyerrors.rs b/pyo3-ffi/src/cpython/pyerrors.rs
index 3058be47c7b..34497676fc5 100644
--- a/pyo3-ffi/src/cpython/pyerrors.rs
+++ b/pyo3-ffi/src/cpython/pyerrors.rs
@@ -1,17 +1,26 @@
-use crate::{PyObject, Py_ssize_t};
+use crate::PyObject;
+#[cfg(not(PyPy))]
+use crate::Py_ssize_t;
 
 #[repr(C)]
 #[derive(Debug)]
 pub struct PyBaseExceptionObject {
     pub ob_base: PyObject,
+    #[cfg(not(PyPy))]
     pub dict: *mut PyObject,
+    #[cfg(not(PyPy))]
     pub args: *mut PyObject,
+    #[cfg(not(PyPy))]
     pub traceback: *mut PyObject,
+    #[cfg(not(PyPy))]
     pub context: *mut PyObject,
+    #[cfg(not(PyPy))]
     pub cause: *mut PyObject,
+    #[cfg(not(PyPy))]
     pub suppress_context: char,
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Debug)]
 pub struct PySyntaxErrorObject {
@@ -28,6 +37,7 @@ pub struct PySyntaxErrorObject {
     pub print_file_and_line: *mut PyObject,
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Debug)]
 pub struct PyImportErrorObject {
@@ -37,6 +47,7 @@ pub struct PyImportErrorObject {
     pub path: *mut PyObject,
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Debug)]
 pub struct PyUnicodeErrorObject {
@@ -48,6 +59,7 @@ pub struct PyUnicodeErrorObject {
     pub reason: *mut PyObject,
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Debug)]
 pub struct PySystemExitObject {
@@ -55,6 +67,7 @@ pub struct PySystemExitObject {
     pub code: *mut PyObject,
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Debug)]
 pub struct PyOSErrorObject {
diff --git a/pyo3-ffi/src/cpython/pymem.rs b/pyo3-ffi/src/cpython/pymem.rs
index 7c07d5c9f1d..2dfb3f3bcfa 100644
--- a/pyo3-ffi/src/cpython/pymem.rs
+++ b/pyo3-ffi/src/cpython/pymem.rs
@@ -26,7 +26,7 @@ pub enum PyMemAllocatorDomain {
 }
 
 // skipped PyMemAllocatorName
-
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct PyMemAllocatorEx {
@@ -40,7 +40,10 @@ pub struct PyMemAllocatorEx {
 }
 
 extern "C" {
+    #[cfg(not(PyPy))]
     pub fn PyMem_GetAllocator(domain: PyMemAllocatorDomain, allocator: *mut PyMemAllocatorEx);
+    #[cfg(not(PyPy))]
     pub fn PyMem_SetAllocator(domain: PyMemAllocatorDomain, allocator: *mut PyMemAllocatorEx);
+    #[cfg(not(PyPy))]
     pub fn PyMem_SetupDebugHooks();
 }
diff --git a/pyo3-ffi/src/cpython/pystate.rs b/pyo3-ffi/src/cpython/pystate.rs
index 19f3a3d0a97..2dcd6958019 100644
--- a/pyo3-ffi/src/cpython/pystate.rs
+++ b/pyo3-ffi/src/cpython/pystate.rs
@@ -27,6 +27,7 @@ pub const PyTrace_OPCODE: c_int = 7;
 // skipped PyTraceInfo
 // skipped CFrame
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Clone, Copy)]
 pub struct _PyErr_StackItem {
diff --git a/pyo3-ffi/src/cpython/pythonrun.rs b/pyo3-ffi/src/cpython/pythonrun.rs
index ba86fe335f8..a92528b7fdc 100644
--- a/pyo3-ffi/src/cpython/pythonrun.rs
+++ b/pyo3-ffi/src/cpython/pythonrun.rs
@@ -1,8 +1,8 @@
 use crate::object::*;
-#[cfg(all(not(Py_LIMITED_API), not(Py_3_10)))]
+#[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
 use crate::pyarena::PyArena;
 use crate::PyCompilerFlags;
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 use crate::{_mod, _node};
 use libc::FILE;
 use std::os::raw::{c_char, c_int};
@@ -54,7 +54,7 @@ extern "C" {
         flags: *mut PyCompilerFlags,
     ) -> c_int;
 
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyParser_ASTFromString(
         s: *const c_char,
         filename: *const c_char,
@@ -62,7 +62,7 @@ extern "C" {
         flags: *mut PyCompilerFlags,
         arena: *mut PyArena,
     ) -> *mut _mod;
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyParser_ASTFromStringObject(
         s: *const c_char,
         filename: *mut PyObject,
@@ -70,7 +70,7 @@ extern "C" {
         flags: *mut PyCompilerFlags,
         arena: *mut PyArena,
     ) -> *mut _mod;
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyParser_ASTFromFile(
         fp: *mut FILE,
         filename: *const c_char,
@@ -82,7 +82,7 @@ extern "C" {
         errcode: *mut c_int,
         arena: *mut PyArena,
     ) -> *mut _mod;
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     pub fn PyParser_ASTFromFileObject(
         fp: *mut FILE,
         filename: *mut PyObject,
@@ -218,14 +218,14 @@ extern "C" {
 // skipped macro PyRun_AnyFileFlags
 
 extern "C" {
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     #[cfg_attr(Py_3_9, deprecated(note = "Python 3.9"))]
     pub fn PyParser_SimpleParseStringFlags(
         arg1: *const c_char,
         arg2: c_int,
         arg3: c_int,
     ) -> *mut _node;
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     #[cfg_attr(Py_3_9, deprecated(note = "Python 3.9"))]
     pub fn PyParser_SimpleParseStringFlagsFilename(
         arg1: *const c_char,
@@ -233,7 +233,7 @@ extern "C" {
         arg3: c_int,
         arg4: c_int,
     ) -> *mut _node;
-    #[cfg(not(Py_3_10))]
+    #[cfg(not(any(PyPy, Py_3_10)))]
     #[cfg_attr(Py_3_9, deprecated(note = "Python 3.9"))]
     pub fn PyParser_SimpleParseFileFlags(
         arg1: *mut FILE,
diff --git a/pyo3-ffi/src/cpython/unicodeobject.rs b/pyo3-ffi/src/cpython/unicodeobject.rs
index 0fa355f93e9..cc9ec4aaf80 100644
--- a/pyo3-ffi/src/cpython/unicodeobject.rs
+++ b/pyo3-ffi/src/cpython/unicodeobject.rs
@@ -1,4 +1,6 @@
-use crate::{PyObject, Py_UCS1, Py_UCS2, Py_UCS4, Py_UNICODE, Py_hash_t, Py_ssize_t};
+#[cfg(not(PyPy))]
+use crate::Py_hash_t;
+use crate::{PyObject, Py_UCS1, Py_UCS2, Py_UCS4, Py_UNICODE, Py_ssize_t};
 use libc::wchar_t;
 use std::os::raw::{c_char, c_int, c_uint, c_void};
 
@@ -32,6 +34,7 @@ use std::os::raw::{c_char, c_int, c_uint, c_void};
 pub struct PyASCIIObject {
     pub ob_base: PyObject,
     pub length: Py_ssize_t,
+    #[cfg(not(PyPy))]
     pub hash: Py_hash_t,
     /// A bit field with various properties.
     ///
diff --git a/pyo3-ffi/src/datetime.rs b/pyo3-ffi/src/datetime.rs
index 166a8f314b8..112d9b24563 100644
--- a/pyo3-ffi/src/datetime.rs
+++ b/pyo3-ffi/src/datetime.rs
@@ -11,12 +11,13 @@
 
 use crate::{PyObject, PyObject_TypeCheck, PyTypeObject, Py_TYPE};
 use std::cell::UnsafeCell;
-use std::os::raw::{c_char, c_int, c_uchar};
+use std::os::raw::{c_char, c_int};
 use std::ptr;
 #[cfg(not(PyPy))]
 use {
     crate::{PyCapsule_Import, Py_hash_t},
     std::ffi::CString,
+    std::os::raw::c_uchar,
 };
 
 // Type struct wrappers
@@ -39,6 +40,7 @@ pub struct PyDateTime_Delta {
 // skipped non-limited PyDateTime_TZInfo
 // skipped non-limited _PyDateTime_BaseTZInfo
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Debug, Copy, Clone)]
 /// Structure representing a `datetime.time` without a `tzinfo` member.
@@ -56,11 +58,6 @@ pub struct _PyDateTime_BaseTime {
 #[repr(C)]
 #[derive(Debug, Copy, Clone)]
 /// Structure representing a `datetime.time`.
-///
-/// # Safety
-///
-/// Care should be taken when reading the `tzinfo` field of this type. If the time does not have a
-/// tzinfo then the Python interpreter is free to allocate it as a [_PyDateTime_BaseTime].
 pub struct PyDateTime_Time {
     pub ob_base: PyObject,
     #[cfg(not(PyPy))]
@@ -70,6 +67,10 @@ pub struct PyDateTime_Time {
     pub data: [c_uchar; _PyDateTime_TIME_DATASIZE],
     #[cfg(not(PyPy))]
     pub fold: c_uchar,
+    /// # Safety
+    ///
+    /// Care should be taken when reading this field. If the time does not have a
+    /// tzinfo then CPython may allocate as a `_PyDateTime_BaseTime` without this field.
     pub tzinfo: *mut PyObject,
 }
 
@@ -80,10 +81,13 @@ pub struct PyDateTime_Date {
     pub ob_base: PyObject,
     #[cfg(not(PyPy))]
     pub hashcode: Py_hash_t,
+    #[cfg(not(PyPy))]
     pub hastzinfo: c_char,
+    #[cfg(not(PyPy))]
     pub data: [c_uchar; _PyDateTime_DATE_DATASIZE],
 }
 
+#[cfg(not(PyPy))]
 #[repr(C)]
 #[derive(Debug, Copy, Clone)]
 /// Structure representing a `datetime.datetime` without a `tzinfo` member.
@@ -101,11 +105,6 @@ pub struct _PyDateTime_BaseDateTime {
 #[repr(C)]
 #[derive(Debug, Copy, Clone)]
 /// Structure representing a `datetime.datetime`.
-///
-/// # Safety
-///
-/// Care should be taken when reading the `tzinfo` field of this type. If the datetime does not have a
-/// tzinfo then the Python interpreter is free to allocate it as a [_PyDateTime_BaseDateTime].
 pub struct PyDateTime_DateTime {
     pub ob_base: PyObject,
     #[cfg(not(PyPy))]
@@ -115,6 +114,10 @@ pub struct PyDateTime_DateTime {
     pub data: [c_uchar; _PyDateTime_DATETIME_DATASIZE],
     #[cfg(not(PyPy))]
     pub fold: c_uchar,
+    /// # Safety
+    ///
+    /// Care should be taken when reading this field. If the time does not have a
+    /// tzinfo then CPython may allocate as a `_PyDateTime_BaseDateTime` without this field.
     pub tzinfo: *mut PyObject,
 }
 
@@ -368,7 +371,8 @@ extern "C" {
     pub fn PyDateTime_DATE_GET_SECOND(o: *mut PyObject) -> c_int;
     #[link_name = "PyPyDateTime_DATE_GET_MICROSECOND"]
     pub fn PyDateTime_DATE_GET_MICROSECOND(o: *mut PyObject) -> c_int;
-    // skipped PyDateTime_DATE_GET_FOLD (not in PyPy)
+    #[link_name = "PyPyDateTime_GET_FOLD"]
+    pub fn PyDateTime_DATE_GET_FOLD(o: *mut PyObject) -> c_int;
     // skipped PyDateTime_DATE_GET_TZINFO (not in PyPy)
 
     #[link_name = "PyPyDateTime_TIME_GET_HOUR"]
@@ -379,7 +383,8 @@ extern "C" {
     pub fn PyDateTime_TIME_GET_SECOND(o: *mut PyObject) -> c_int;
     #[link_name = "PyPyDateTime_TIME_GET_MICROSECOND"]
     pub fn PyDateTime_TIME_GET_MICROSECOND(o: *mut PyObject) -> c_int;
-    // skipped PyDateTime_TIME_GET_FOLD (not in PyPy)
+    #[link_name = "PyPyDateTime_TIME_GET_FOLD"]
+    pub fn PyDateTime_TIME_GET_FOLD(o: *mut PyObject) -> c_int;
     // skipped PyDateTime_TIME_GET_TZINFO (not in PyPy)
 
     #[link_name = "PyPyDateTime_DELTA_GET_DAYS"]
@@ -441,7 +446,6 @@ pub struct PyDateTime_CAPI {
     ) -> *mut PyObject,
     pub Date_FromTimestamp:
         unsafe extern "C" fn(cls: *mut PyTypeObject, args: *mut PyObject) -> *mut PyObject,
-    #[cfg(not(PyPy))]
     pub DateTime_FromDateAndTimeAndFold: unsafe extern "C" fn(
         year: c_int,
         month: c_int,
@@ -454,7 +458,6 @@ pub struct PyDateTime_CAPI {
         fold: c_int,
         cls: *mut PyTypeObject,
     ) -> *mut PyObject,
-    #[cfg(not(PyPy))]
     pub Time_FromTimeAndFold: unsafe extern "C" fn(
         hour: c_int,
         minute: c_int,
diff --git a/pyo3-ffi/src/lib.rs b/pyo3-ffi/src/lib.rs
index 04ad398c8bb..1e3ee85596e 100644
--- a/pyo3-ffi/src/lib.rs
+++ b/pyo3-ffi/src/lib.rs
@@ -314,7 +314,7 @@ pub use self::moduleobject::*;
 pub use self::object::*;
 pub use self::objimpl::*;
 pub use self::osmodule::*;
-#[cfg(not(any(Py_LIMITED_API, Py_3_10)))]
+#[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
 pub use self::pyarena::*;
 pub use self::pycapsule::*;
 pub use self::pyerrors::*;
@@ -395,7 +395,7 @@ mod osmodule;
 // skipped picklebufobject.h
 // skipped pyctype.h
 // skipped py_curses.h
-#[cfg(not(any(Py_LIMITED_API, Py_3_10)))]
+#[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
 mod pyarena;
 mod pycapsule;
 // skipped pydecimal.h
diff --git a/pyo3-ffi/src/objimpl.rs b/pyo3-ffi/src/objimpl.rs
index deeaceb1518..2a3307e6c2f 100644
--- a/pyo3-ffi/src/objimpl.rs
+++ b/pyo3-ffi/src/objimpl.rs
@@ -39,25 +39,27 @@ extern "C" {
     pub fn PyGC_IsEnabled() -> c_int;
 }
 
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 #[repr(C)]
 #[derive(Copy, Clone)]
-#[cfg(not(Py_LIMITED_API))]
 pub struct PyObjectArenaAllocator {
     pub ctx: *mut c_void,
     pub alloc: Option<extern "C" fn(ctx: *mut c_void, size: size_t) -> *mut c_void>,
     pub free: Option<extern "C" fn(ctx: *mut c_void, ptr: *mut c_void, size: size_t)>,
 }
 
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 impl Default for PyObjectArenaAllocator {
     #[inline]
     fn default() -> Self {
         unsafe { std::mem::zeroed() }
     }
 }
-#[cfg(not(Py_LIMITED_API))]
+
 extern "C" {
+    #[cfg(not(any(Py_LIMITED_API, PyPy)))]
     pub fn PyObject_GetArenaAllocator(allocator: *mut PyObjectArenaAllocator);
+    #[cfg(not(any(Py_LIMITED_API, PyPy)))]
     pub fn PyObject_SetArenaAllocator(allocator: *mut PyObjectArenaAllocator);
 }
 
diff --git a/pyo3-ffi/src/pyhash.rs b/pyo3-ffi/src/pyhash.rs
index bfff7341bcd..f8072d85108 100644
--- a/pyo3-ffi/src/pyhash.rs
+++ b/pyo3-ffi/src/pyhash.rs
@@ -1,6 +1,6 @@
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 use crate::pyport::{Py_hash_t, Py_ssize_t};
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 use std::os::raw::{c_char, c_void};
 
 use std::os::raw::{c_int, c_ulong};
@@ -20,7 +20,7 @@ pub const _PyHASH_MULTIPLIER: c_ulong = 1000003;
 
 // skipped non-limited _Py_HashSecret_t
 
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 #[repr(C)]
 #[derive(Copy, Clone)]
 pub struct PyHash_FuncDef {
@@ -30,7 +30,7 @@ pub struct PyHash_FuncDef {
     pub seed_bits: c_int,
 }
 
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 impl Default for PyHash_FuncDef {
     #[inline]
     fn default() -> Self {
diff --git a/pyo3-ffi/src/pythonrun.rs b/pyo3-ffi/src/pythonrun.rs
index d37842367af..196cf5354e5 100644
--- a/pyo3-ffi/src/pythonrun.rs
+++ b/pyo3-ffi/src/pythonrun.rs
@@ -1,13 +1,12 @@
 use crate::object::*;
-#[cfg(all(not(Py_LIMITED_API), not(Py_3_10)))]
+#[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
 use libc::FILE;
-#[cfg(any(Py_LIMITED_API, not(Py_3_10)))]
+#[cfg(all(not(PyPy), any(Py_LIMITED_API, not(Py_3_10))))]
 use std::os::raw::c_char;
 use std::os::raw::c_int;
 
 extern "C" {
-    #[cfg(Py_LIMITED_API)]
-    #[cfg(not(PyPy))]
+    #[cfg(all(Py_LIMITED_API, not(PyPy)))]
     pub fn Py_CompileString(string: *const c_char, p: *const c_char, s: c_int) -> *mut PyObject;
 
     #[cfg_attr(PyPy, link_name = "PyPyErr_Print")]
@@ -24,15 +23,15 @@ pub const PYOS_STACK_MARGIN: c_int = 2048;
 
 // skipped PyOS_CheckStack under Microsoft C
 
-#[cfg(all(not(Py_LIMITED_API), not(Py_3_10)))]
+#[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
 opaque_struct!(_mod);
 
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 opaque_struct!(symtable);
-#[cfg(not(Py_3_10))]
+#[cfg(not(any(PyPy, Py_3_10)))]
 opaque_struct!(_node);
 
-#[cfg(all(not(Py_LIMITED_API), not(Py_3_10)))]
+#[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
 #[cfg_attr(Py_3_9, deprecated(note = "Python 3.9"))]
 #[inline]
 pub unsafe fn PyParser_SimpleParseString(s: *const c_char, b: c_int) -> *mut _node {
@@ -40,7 +39,7 @@ pub unsafe fn PyParser_SimpleParseString(s: *const c_char, b: c_int) -> *mut _no
     crate::PyParser_SimpleParseStringFlags(s, b, 0)
 }
 
-#[cfg(all(not(Py_LIMITED_API), not(Py_3_10)))]
+#[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
 #[cfg_attr(Py_3_9, deprecated(note = "Python 3.9"))]
 #[inline]
 pub unsafe fn PyParser_SimpleParseFile(fp: *mut FILE, s: *const c_char, b: c_int) -> *mut _node {
@@ -55,7 +54,7 @@ extern "C" {
         filename: *const c_char,
         start: c_int,
     ) -> *mut symtable;
-    #[cfg(not(any(Py_LIMITED_API, Py_3_10, PyPy)))]
+    #[cfg(not(any(PyPy, Py_LIMITED_API, Py_3_10)))]
     pub fn Py_SymtableStringObject(
         str: *const c_char,
         filename: *mut PyObject,
diff --git a/pyo3-ffi/src/setobject.rs b/pyo3-ffi/src/setobject.rs
index c90d26f5d65..c629709529f 100644
--- a/pyo3-ffi/src/setobject.rs
+++ b/pyo3-ffi/src/setobject.rs
@@ -1,12 +1,12 @@
 use crate::object::*;
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 use crate::pyport::Py_hash_t;
 use crate::pyport::Py_ssize_t;
 use std::os::raw::c_int;
 
 pub const PySet_MINSIZE: usize = 8;
 
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 #[repr(C)]
 #[derive(Debug)]
 pub struct setentry {
@@ -14,7 +14,7 @@ pub struct setentry {
     pub hash: Py_hash_t,
 }
 
-#[cfg(not(Py_LIMITED_API))]
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
 #[repr(C)]
 #[derive(Debug)]
 pub struct PySetObject {
diff --git a/pyo3-ffi/src/weakrefobject.rs b/pyo3-ffi/src/weakrefobject.rs
index b9506115a4b..fd5f83aae8d 100644
--- a/pyo3-ffi/src/weakrefobject.rs
+++ b/pyo3-ffi/src/weakrefobject.rs
@@ -1,6 +1,7 @@
 use crate::object::*;
 use std::os::raw::c_int;
 
+#[cfg(not(PyPy))]
 opaque_struct!(PyWeakReference);
 
 extern "C" {
diff --git a/pytests/src/datetime.rs b/pytests/src/datetime.rs
index b21d3e6931b..b0a306ec821 100644
--- a/pytests/src/datetime.rs
+++ b/pytests/src/datetime.rs
@@ -43,7 +43,6 @@ fn make_time<'p>(
     )
 }
 
-#[cfg(not(PyPy))]
 #[pyfunction]
 fn time_with_fold<'p>(
     py: Python<'p>,
@@ -78,7 +77,6 @@ fn get_time_tuple<'p>(py: Python<'p>, dt: &PyTime) -> &'p PyTuple {
     )
 }
 
-#[cfg(not(PyPy))]
 #[pyfunction]
 fn get_time_tuple_fold<'p>(py: Python<'p>, dt: &PyTime) -> &'p PyTuple {
     PyTuple::new(
@@ -152,7 +150,6 @@ fn get_datetime_tuple<'p>(py: Python<'p>, dt: &PyDateTime) -> &'p PyTuple {
     )
 }
 
-#[cfg(not(PyPy))]
 #[pyfunction]
 fn get_datetime_tuple_fold<'p>(py: Python<'p>, dt: &PyDateTime) -> &'p PyTuple {
     PyTuple::new(
@@ -227,13 +224,9 @@ pub fn datetime(_py: Python<'_>, m: &PyModule) -> PyResult<()> {
     m.add_function(wrap_pyfunction!(get_datetime_tzinfo, m)?)?;
     m.add_function(wrap_pyfunction!(get_time_tzinfo, m)?)?;
 
-    // Functions not supported by PyPy
-    #[cfg(not(PyPy))]
-    {
-        m.add_function(wrap_pyfunction!(time_with_fold, m)?)?;
-        m.add_function(wrap_pyfunction!(get_time_tuple_fold, m)?)?;
-        m.add_function(wrap_pyfunction!(get_datetime_tuple_fold, m)?)?;
-    }
+    m.add_function(wrap_pyfunction!(time_with_fold, m)?)?;
+    m.add_function(wrap_pyfunction!(get_time_tuple_fold, m)?)?;
+    m.add_function(wrap_pyfunction!(get_datetime_tuple_fold, m)?)?;
 
     m.add_class::<TzClass>()?;
 
diff --git a/src/exceptions.rs b/src/exceptions.rs
index fb4be1e4356..4a4d60ef6d9 100644
--- a/src/exceptions.rs
+++ b/src/exceptions.rs
@@ -395,12 +395,15 @@ impl_native_exception!(
     PyExc_FloatingPointError,
     native_doc!("FloatingPointError")
 );
+#[cfg(not(PyPy))]
 impl_native_exception!(
     PyOSError,
     PyExc_OSError,
     native_doc!("OSError"),
     ffi::PyOSErrorObject
 );
+#[cfg(PyPy)]
+impl_native_exception!(PyOSError, PyExc_OSError, native_doc!("OSError"));
 impl_native_exception!(PyImportError, PyExc_ImportError, native_doc!("ImportError"));
 
 impl_native_exception!(
@@ -438,36 +441,49 @@ impl_native_exception!(
     PyExc_NotImplementedError,
     native_doc!("NotImplementedError")
 );
+#[cfg(not(PyPy))]
 impl_native_exception!(
     PySyntaxError,
     PyExc_SyntaxError,
     native_doc!("SyntaxError"),
     ffi::PySyntaxErrorObject
 );
+#[cfg(PyPy)]
+impl_native_exception!(PySyntaxError, PyExc_SyntaxError, native_doc!("SyntaxError"));
 impl_native_exception!(
     PyReferenceError,
     PyExc_ReferenceError,
     native_doc!("ReferenceError")
 );
 impl_native_exception!(PySystemError, PyExc_SystemError, native_doc!("SystemError"));
+#[cfg(not(PyPy))]
 impl_native_exception!(
     PySystemExit,
     PyExc_SystemExit,
     native_doc!("SystemExit"),
     ffi::PySystemExitObject
 );
+#[cfg(PyPy)]
+impl_native_exception!(PySystemExit, PyExc_SystemExit, native_doc!("SystemExit"));
 impl_native_exception!(PyTypeError, PyExc_TypeError, native_doc!("TypeError"));
 impl_native_exception!(
     PyUnboundLocalError,
     PyExc_UnboundLocalError,
     native_doc!("UnboundLocalError")
 );
+#[cfg(not(PyPy))]
 impl_native_exception!(
     PyUnicodeError,
     PyExc_UnicodeError,
     native_doc!("UnicodeError"),
     ffi::PyUnicodeErrorObject
 );
+#[cfg(PyPy)]
+impl_native_exception!(
+    PyUnicodeError,
+    PyExc_UnicodeError,
+    native_doc!("UnicodeError")
+);
 // these three errors need arguments, so they're too annoying to write tests for using macros...
 impl_native_exception!(
     PyUnicodeDecodeError,
diff --git a/src/ffi/tests.rs b/src/ffi/tests.rs
index 0231b0ffcd7..8508e6df338 100644
--- a/src/ffi/tests.rs
+++ b/src/ffi/tests.rs
@@ -67,6 +67,7 @@ fn ascii_object_bitfield() {
     let mut o = PyASCIIObject {
         ob_base,
         length: 0,
+        #[cfg(not(PyPy))]
         hash: 0,
         state: 0,
         wstr: std::ptr::null_mut() as *mut wchar_t,
diff --git a/src/types/datetime.rs b/src/types/datetime.rs
index 2edcc0e780c..2d55caca9b8 100644
--- a/src/types/datetime.rs
+++ b/src/types/datetime.rs
@@ -7,19 +7,17 @@ use crate::err::PyResult;
 use crate::ffi::{
     self, PyDateTime_CAPI, PyDateTime_FromTimestamp, PyDateTime_IMPORT, PyDate_FromTimestamp,
 };
-#[cfg(not(PyPy))]
-use crate::ffi::{PyDateTime_DATE_GET_FOLD, PyDateTime_TIME_GET_FOLD};
 use crate::ffi::{
-    PyDateTime_DATE_GET_HOUR, PyDateTime_DATE_GET_MICROSECOND, PyDateTime_DATE_GET_MINUTE,
-    PyDateTime_DATE_GET_SECOND,
+    PyDateTime_DATE_GET_FOLD, PyDateTime_DATE_GET_HOUR, PyDateTime_DATE_GET_MICROSECOND,
+    PyDateTime_DATE_GET_MINUTE, PyDateTime_DATE_GET_SECOND,
 };
 use crate::ffi::{
     PyDateTime_DELTA_GET_DAYS, PyDateTime_DELTA_GET_MICROSECONDS, PyDateTime_DELTA_GET_SECONDS,
 };
 use crate::ffi::{PyDateTime_GET_DAY, PyDateTime_GET_MONTH, PyDateTime_GET_YEAR};
 use crate::ffi::{
-    PyDateTime_TIME_GET_HOUR, PyDateTime_TIME_GET_MICROSECOND, PyDateTime_TIME_GET_MINUTE,
-    PyDateTime_TIME_GET_SECOND,
+    PyDateTime_TIME_GET_FOLD, PyDateTime_TIME_GET_HOUR, PyDateTime_TIME_GET_MICROSECOND,
+    PyDateTime_TIME_GET_MINUTE, PyDateTime_TIME_GET_SECOND,
 };
 use crate::instance::PyNativeType;
 use crate::types::PyTuple;
@@ -156,7 +154,6 @@ pub trait PyTimeAccess {
     /// This typically occurs at the end of daylight savings time. Only valid if the
     /// represented time is ambiguous.
     /// See [PEP 495](https://www.python.org/dev/peps/pep-0495/) for more detail.
-    #[cfg(not(PyPy))]
     fn get_fold(&self) -> bool;
 }
 
@@ -273,7 +270,6 @@ impl PyDateTime {
     /// This typically occurs at the end of daylight savings time. Only valid if the
     /// represented time is ambiguous.
     /// See [PEP 495](https://www.python.org/dev/peps/pep-0495/) for more detail.
-    #[cfg(not(PyPy))]
     #[allow(clippy::too_many_arguments)]
     pub fn new_with_fold<'p>(
         py: Python<'p>,
@@ -363,7 +359,6 @@ impl PyTimeAccess for PyDateTime {
         unsafe { PyDateTime_DATE_GET_MICROSECOND(self.as_ptr()) as u32 }
     }
 
-    #[cfg(not(PyPy))]
     fn get_fold(&self) -> bool {
         unsafe { PyDateTime_DATE_GET_FOLD(self.as_ptr()) > 0 }
     }
@@ -417,7 +412,6 @@ impl PyTime {
         }
     }
 
-    #[cfg(not(PyPy))]
     /// Alternate constructor that takes a `fold` argument. See [`PyDateTime::new_with_fold`].
     pub fn new_with_fold<'p>(
         py: Python<'p>,
@@ -461,7 +455,6 @@ impl PyTimeAccess for PyTime {
         unsafe { PyDateTime_TIME_GET_MICROSECOND(self.as_ptr()) as u32 }
     }
 
-    #[cfg(not(PyPy))]
     fn get_fold(&self) -> bool {
         unsafe { PyDateTime_TIME_GET_FOLD(self.as_ptr()) != 0 }
     }
@@ -552,7 +545,6 @@ fn opt_to_pyobj(py: Python<'_>, opt: Option<&PyObject>) -> *mut ffi::PyObject {
 
 #[cfg(test)]
 mod tests {
-    #[cfg(not(PyPy))]
     #[test]
     fn test_new_with_fold() {
         crate::Python::with_gil(|py| {
diff --git a/src/types/frozenset.rs b/src/types/frozenset.rs
index d85842940c4..cfe6348fb16 100644
--- a/src/types/frozenset.rs
+++ b/src/types/frozenset.rs
@@ -12,6 +12,7 @@ use std::ptr;
 #[repr(transparent)]
 pub struct PyFrozenSet(PyAny);
 
+#[cfg(not(PyPy))]
 pyobject_native_type!(
     PyFrozenSet,
     ffi::PySetObject,
@@ -19,6 +20,13 @@ pyobject_native_type!(
     #checkfunction=ffi::PyFrozenSet_Check
 );
 
+#[cfg(PyPy)]
+pyobject_native_type_core!(
+    PyFrozenSet,
+    ffi::PyFrozenSet_Type,
+    #checkfunction=ffi::PyFrozenSet_Check
+);
+
 impl PyFrozenSet {
     /// Creates a new frozenset.
     ///
diff --git a/src/types/set.rs b/src/types/set.rs
index 7390807736c..b083c476128 100644
--- a/src/types/set.rs
+++ b/src/types/set.rs
@@ -13,7 +13,20 @@ use std::{collections, hash, ptr};
 #[repr(transparent)]
 pub struct PySet(PyAny);
 
-pyobject_native_type!(PySet, ffi::PySetObject, ffi::PySet_Type, #checkfunction=ffi::PySet_Check);
+#[cfg(not(PyPy))]
+pyobject_native_type!(
+    PySet,
+    ffi::PySetObject,
+    ffi::PySet_Type,
+    #checkfunction=ffi::PySet_Check
+);
+
+#[cfg(PyPy)]
+pyobject_native_type_core!(
+    PySet,
+    ffi::PySet_Type,
+    #checkfunction=ffi::PySet_Check
+);
 
 impl PySet {
     /// Creates a new set with elements from the given slice.
diff --git a/tests/test_inheritance.rs b/tests/test_inheritance.rs
index 25dae983335..f9ab69e56e5 100644
--- a/tests/test_inheritance.rs
+++ b/tests/test_inheritance.rs
@@ -173,25 +173,30 @@ except Exception as e:
 mod inheriting_native_type {
     use super::*;
     use pyo3::exceptions::PyException;
-    use pyo3::types::{IntoPyDict, PyDict, PySet};
+    use pyo3::types::{IntoPyDict, PyDict};
 
-    #[pyclass(extends=PySet)]
-    #[derive(Debug)]
-    struct SetWithName {
-        #[pyo3(get, name = "name")]
-        _name: &'static str,
-    }
+    #[cfg(not(PyPy))]
+    #[test]
+    fn inherit_set() {
+        use pyo3::types::PySet;
+
+        #[cfg(not(PyPy))]
+        #[pyclass(extends=PySet)]
+        #[derive(Debug)]
+        struct SetWithName {
+            #[pyo3(get, name = "name")]
+            _name: &'static str,
+        }
 
-    #[pymethods]
-    impl SetWithName {
-        #[new]
-        fn new() -> Self {
-            SetWithName { _name: "Hello :)" }
+        #[cfg(not(PyPy))]
+        #[pymethods]
+        impl SetWithName {
+            #[new]
+            fn new() -> Self {
+                SetWithName { _name: "Hello :)" }
+            }
         }
-    }
 
-    #[test]
-    fn inherit_set() {
         let gil = Python::acquire_gil();
         let py = gil.python();
         let set_sub = pyo3::PyCell::new(py, SetWithName::new()).unwrap();