diff --git a/crossbeam-epoch/Cargo.toml b/crossbeam-epoch/Cargo.toml
index 79e0f5ec9..2e882bfd7 100644
--- a/crossbeam-epoch/Cargo.toml
+++ b/crossbeam-epoch/Cargo.toml
@@ -39,5 +39,8 @@ optional = true
 version = "1"
 default-features = false
 
+[build-dependencies]
+autocfg = "0.1.6"
+
 [dev-dependencies]
 rand = "0.6"
diff --git a/crossbeam-epoch/build.rs b/crossbeam-epoch/build.rs
new file mode 100644
index 000000000..d451c24b2
--- /dev/null
+++ b/crossbeam-epoch/build.rs
@@ -0,0 +1,8 @@
+extern crate autocfg;
+
+fn main() {
+    let cfg = autocfg::new();
+    if cfg.probe_rustc_version(1, 31) {
+        println!("cargo:rustc-cfg=has_min_const_fn");
+    }
+}
diff --git a/crossbeam-epoch/src/atomic.rs b/crossbeam-epoch/src/atomic.rs
index 0444c118b..a2044740b 100644
--- a/crossbeam-epoch/src/atomic.rs
+++ b/crossbeam-epoch/src/atomic.rs
@@ -150,7 +150,7 @@ impl<T> Atomic<T> {
     ///
     /// let a = Atomic::<i32>::null();
     /// ```
-    #[cfg(not(feature = "nightly"))]
+    #[cfg(not(has_min_const_fn))]
     pub fn null() -> Atomic<T> {
         Self {
             data: AtomicUsize::new(0),
@@ -167,7 +167,7 @@ impl<T> Atomic<T> {
     ///
     /// let a = Atomic::<i32>::null();
     /// ```
-    #[cfg(feature = "nightly")]
+    #[cfg(has_min_const_fn)]
     pub const fn null() -> Atomic<T> {
         Self {
             data: AtomicUsize::new(0),
diff --git a/crossbeam-epoch/src/lib.rs b/crossbeam-epoch/src/lib.rs
index 112180b25..c5b504e50 100644
--- a/crossbeam-epoch/src/lib.rs
+++ b/crossbeam-epoch/src/lib.rs
@@ -57,7 +57,6 @@
 #![warn(missing_docs)]
 #![warn(missing_debug_implementations)]
 #![cfg_attr(not(feature = "std"), no_std)]
-#![cfg_attr(feature = "nightly", feature(const_fn))]
 #![cfg_attr(feature = "nightly", feature(cfg_target_has_atomic))]
 
 #[macro_use]
diff --git a/crossbeam-utils/Cargo.toml b/crossbeam-utils/Cargo.toml
index 23f049ec1..00f333198 100644
--- a/crossbeam-utils/Cargo.toml
+++ b/crossbeam-utils/Cargo.toml
@@ -25,5 +25,8 @@ alloc = []
 cfg-if = "0.1.2"
 lazy_static = { version = "1.1.0", optional = true }
 
+[build-dependencies]
+autocfg = "0.1.6"
+
 [dev-dependencies]
 rand = "0.6"
diff --git a/crossbeam-utils/build.rs b/crossbeam-utils/build.rs
new file mode 100644
index 000000000..d451c24b2
--- /dev/null
+++ b/crossbeam-utils/build.rs
@@ -0,0 +1,8 @@
+extern crate autocfg;
+
+fn main() {
+    let cfg = autocfg::new();
+    if cfg.probe_rustc_version(1, 31) {
+        println!("cargo:rustc-cfg=has_min_const_fn");
+    }
+}
diff --git a/crossbeam-utils/src/atomic/atomic_cell.rs b/crossbeam-utils/src/atomic/atomic_cell.rs
index 5166a74f2..4fa54c85b 100644
--- a/crossbeam-utils/src/atomic/atomic_cell.rs
+++ b/crossbeam-utils/src/atomic/atomic_cell.rs
@@ -52,12 +52,29 @@ impl<T> AtomicCell<T> {
     ///
     /// let a = AtomicCell::new(7);
     /// ```
+    #[cfg(not(has_min_const_fn))]
     pub fn new(val: T) -> AtomicCell<T> {
         AtomicCell {
             value: UnsafeCell::new(val),
         }
     }
 
+    /// Creates a new atomic cell initialized with `val`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use crossbeam_utils::atomic::AtomicCell;
+    ///
+    /// let a = AtomicCell::new(7);
+    /// ```
+    #[cfg(has_min_const_fn)]
+    pub const fn new(val: T) -> AtomicCell<T> {
+        AtomicCell {
+            value: UnsafeCell::new(val),
+        }
+    }
+
     /// Unwraps the atomic cell and returns its inner value.
     ///
     /// # Examples
diff --git a/crossbeam-utils/tests/atomic_cell.rs b/crossbeam-utils/tests/atomic_cell.rs
index 940619233..57206aeda 100644
--- a/crossbeam-utils/tests/atomic_cell.rs
+++ b/crossbeam-utils/tests/atomic_cell.rs
@@ -223,3 +223,12 @@ fn garbage_padding() {
     assert!(cell.compare_exchange(prev, next).is_ok());
     println!();
 }
+
+#[cfg(has_min_const_fn)]
+#[test]
+fn const_atomic_cell_new() {
+    static CELL: AtomicCell<usize> = AtomicCell::new(0);
+
+    CELL.store(1);
+    assert_eq!(CELL.load(), 1);
+}