diff --git a/hypothesis-python/RELEASE.rst b/hypothesis-python/RELEASE.rst
new file mode 100644
index 0000000000..b4a4e4d498
--- /dev/null
+++ b/hypothesis-python/RELEASE.rst
@@ -0,0 +1,7 @@
+RELEASE_TYPE: patch
+
+This patch fixes an issue where :func:`~hypothesis.strategies.builds` could not be used with :pypi:`attrs` objects that defined private attributes (i.e. attributes with a leading underscore). See also :issue:`3791`.
+
+This patch also adds support more generally for using :func:`~hypothesis.strategies.builds` with attrs' ``alias`` parameter, which was previously unsupported.
+
+This patch increases the minimum required version of attrs to 22.2.0.
diff --git a/hypothesis-python/setup.py b/hypothesis-python/setup.py
index 5f5e82d1f0..d4054fd5af 100644
--- a/hypothesis-python/setup.py
+++ b/hypothesis-python/setup.py
@@ -96,7 +96,7 @@ def local_file(name):
     zip_safe=False,
     extras_require=extras,
     install_requires=[
-        "attrs>=19.2.0",
+        "attrs>=22.2.0",
         "exceptiongroup>=1.0.0 ; python_version<'3.11'",
         "sortedcontainers>=2.1.0,<3.0.0",
     ],
diff --git a/hypothesis-python/src/hypothesis/strategies/_internal/attrs.py b/hypothesis-python/src/hypothesis/strategies/_internal/attrs.py
index d4f56a1f3a..3b08f3a43d 100644
--- a/hypothesis-python/src/hypothesis/strategies/_internal/attrs.py
+++ b/hypothesis-python/src/hypothesis/strategies/_internal/attrs.py
@@ -21,12 +21,38 @@
 from hypothesis.utils.conventions import infer
 
 
+def get_attribute_by_alias(fields, alias, *, target=None):
+    """
+    Get an attrs attribute by its alias, rather than its name (compare
+    getattr(fields, name)).
+
+    ``target`` is used only to provide a nicer error message, and can be safely
+    omitted.
+    """
+    # attrs supports defining an alias for a field, which is the name used when
+    # defining __init__. The init args are what we pull from when determining
+    # what parameters we need to supply to the class, so it's what we need to
+    # match against as well, rather than the class-level attribute name.
+    matched_fields = [f for f in fields if f.alias == alias]
+    if not matched_fields:
+        raise TypeError(
+            f"Unexpected keyword argument {alias} for attrs class"
+            f"{f' {target}' if target else ''}. Expected one of "
+            f"{[f.name for f in fields]}"
+        )
+    # alias is used as an arg in __init__, so it is guaranteed to be unique, if
+    # it exists.
+    assert len(matched_fields) == 1
+    return matched_fields[0]
+
+
 def from_attrs(target, args, kwargs, to_infer):
     """An internal version of builds(), specialised for Attrs classes."""
     fields = attr.fields(target)
     kwargs = {k: v for k, v in kwargs.items() if v is not infer}
     for name in to_infer:
-        kwargs[name] = from_attrs_attribute(getattr(fields, name), target)
+        attrib = get_attribute_by_alias(fields, name, target=target)
+        kwargs[name] = from_attrs_attribute(attrib, target)
     # We might make this strategy more efficient if we added a layer here that
     # retries drawing if validation fails, for improved composition.
     # The treatment of timezones in datetimes() provides a precedent.
diff --git a/hypothesis-python/tests/cover/test_attrs_inference.py b/hypothesis-python/tests/cover/test_attrs_inference.py
index 6dce6a4c00..c517cea883 100644
--- a/hypothesis-python/tests/cover/test_attrs_inference.py
+++ b/hypothesis-python/tests/cover/test_attrs_inference.py
@@ -89,3 +89,37 @@ def test_cannot_infer(c):
 def test_cannot_infer_takes_self():
     with pytest.raises(ResolutionFailed):
         st.builds(Inferrables, has_default_factory_takes_self=...).example()
+
+
+@attr.s
+class HasPrivateAttribute:
+    _x: int = attr.ib()
+
+
+@pytest.mark.parametrize("s", [st.just(42), ...])
+def test_private_attribute(s):
+    st.builds(HasPrivateAttribute, x=s).example()
+
+
+def test_private_attribute_underscore_fails():
+    with pytest.raises(TypeError, match="unexpected keyword argument '_x'"):
+        st.builds(HasPrivateAttribute, _x=st.just(42)).example()
+
+
+def test_private_attribute_underscore_infer_fails():
+    # this has a slightly different failure case, because it goes through
+    # attrs-specific resolution logic.
+    with pytest.raises(
+        TypeError, match="Unexpected keyword argument _x for attrs class"
+    ):
+        st.builds(HasPrivateAttribute, _x=...).example()
+
+
+@attr.s
+class HasAliasedAttribute:
+    x: int = attr.ib(alias="crazyname")
+
+
+@pytest.mark.parametrize("s", [st.just(42), ...])
+def test_aliased_attribute(s):
+    st.builds(HasAliasedAttribute, crazyname=s).example()