diff --git a/hypothesis-python/RELEASE.rst b/hypothesis-python/RELEASE.rst
new file mode 100644
index 0000000000..590b76ffda
--- /dev/null
+++ b/hypothesis-python/RELEASE.rst
@@ -0,0 +1,5 @@
+RELEASE_TYPE: minor
+
+This preserves the type annotations of functions passed to :func:`hypothesis.strategies.composite` and :func:`hypothesis.strategies.functions` by using :obj:`python:typing.ParamSpec`.
+
+This improves the ability of static type-checkers to check test code that uses Hypothesis, and improves auto-completion in IDEs.
\ No newline at end of file
diff --git a/hypothesis-python/src/hypothesis/core.py b/hypothesis-python/src/hypothesis/core.py
index 6c3f838d5b..0dd11e3042 100644
--- a/hypothesis-python/src/hypothesis/core.py
+++ b/hypothesis-python/src/hypothesis/core.py
@@ -951,9 +951,7 @@ def fuzz_one_input(
 def given(
     *_given_arguments: Union[SearchStrategy, InferType],
     **_given_kwargs: Union[SearchStrategy, InferType],
-) -> Callable[
-    [Callable[..., Union[None, Coroutine[Any, Any, None]]]], Callable[..., None]
-]:
+) -> Callable[[Callable[..., Union[None, Coroutine[Any, Any, None]]]], Callable[..., None]]:
     """A decorator for turning a test function that accepts arguments into a
     randomized test.
 
diff --git a/hypothesis-python/src/hypothesis/strategies/_internal/core.py b/hypothesis-python/src/hypothesis/strategies/_internal/core.py
index 7530ec62d7..4e2225fdef 100644
--- a/hypothesis-python/src/hypothesis/strategies/_internal/core.py
+++ b/hypothesis-python/src/hypothesis/strategies/_internal/core.py
@@ -43,6 +43,7 @@
 from uuid import UUID
 
 import attr
+from typing_extensions import Concatenate
 
 from hypothesis.control import cleanup, note
 from hypothesis.errors import InvalidArgument, ResolutionFailed
@@ -94,6 +95,7 @@
 from hypothesis.strategies._internal.shared import SharedStrategy
 from hypothesis.strategies._internal.strategies import (
     Ex,
+    P,
     SampledFromStrategy,
     T,
     one_of,
@@ -1451,7 +1453,9 @@ def __call__(self, strategy: SearchStrategy[Ex], label: object = None) -> Ex:
 
 
 @cacheable
-def composite(f: Callable[..., Ex]) -> Callable[..., SearchStrategy[Ex]]:
+def composite(
+    f: Callable[Concatenate[DrawFn, P], Ex]
+) -> Callable[P, SearchStrategy[Ex]]:
     """Defines a strategy that is built out of potentially arbitrarily many
     other strategies.
 
@@ -1850,10 +1854,10 @@ def emails() -> SearchStrategy[str]:
 @defines_strategy()
 def functions(
     *,
-    like: Callable[..., Any] = lambda: None,
+    like: Callable[P, Any] = lambda: None,
     returns: Optional[SearchStrategy[Any]] = None,
     pure: bool = False,
-) -> SearchStrategy[Callable[..., Any]]:
+) -> SearchStrategy[Callable[P, Any]]:
     # The proper type signature of `functions()` would have T instead of Any, but mypy
     # disallows default args for generics: https://github.com/python/mypy/issues/3737
     """functions(*, like=lambda: None, returns=none(), pure=False)
diff --git a/hypothesis-python/src/hypothesis/strategies/_internal/strategies.py b/hypothesis-python/src/hypothesis/strategies/_internal/strategies.py
index 680e6b58ce..c3a50ef1fe 100644
--- a/hypothesis-python/src/hypothesis/strategies/_internal/strategies.py
+++ b/hypothesis-python/src/hypothesis/strategies/_internal/strategies.py
@@ -24,6 +24,8 @@
     overload,
 )
 
+from typing_extensions import ParamSpec
+
 from hypothesis._settings import HealthCheck, Phase, Verbosity, settings
 from hypothesis.control import _current_build_context, assume
 from hypothesis.errors import (
@@ -54,6 +56,7 @@
 T3 = TypeVar("T3")
 T4 = TypeVar("T4")
 T5 = TypeVar("T5")
+P = ParamSpec("P")
 
 calculating = UniqueIdentifier("calculating")
 
diff --git a/whole-repo-tests/test_type_hints.py b/whole-repo-tests/test_type_hints.py
index fedf21ad71..7fd318cb77 100644
--- a/whole-repo-tests/test_type_hints.py
+++ b/whole-repo-tests/test_type_hints.py
@@ -142,6 +142,32 @@ def test_drawfn_type_tracing(tmpdir):
     assert got == "str"
 
 
+def test_composite_type_tracing(tmpdir):
+    f = tmpdir.join("check_mypy_on_st_composite.py")
+    f.write(
+        "from hypothesis.strategies import composite, DrawFn\n"
+        "@composite\n"
+        "def comp(draw: DrawFn, x: int) -> int:\n"
+        "    return x\n"
+        "reveal_type(comp)\n"
+    )
+    got = get_mypy_analysed_type(str(f.realpath()), ...)
+    assert got == "def (x: int) -> int"
+
+
+def test_functions_type_tracing(tmpdir):
+    f = tmpdir.join("check_mypy_on_st_functions.py")
+    f.write(
+        "from hypothesis.strategies import functions\n"
+        "def like(x: int, y: str) -> str:\n"
+        "    return str(x) + y\n"
+        "st = functions(like)\n"
+        "reveal_type(st)\n"
+    )
+    got = get_mypy_analysed_type(str(f.realpath()), ...)
+    assert got == "SearchStrategy[Callable[[int, str], str]]"
+
+
 def test_settings_preserves_type(tmpdir):
     f = tmpdir.join("check_mypy_on_settings.py")
     f.write(