diff --git a/CHANGELOG.md b/CHANGELOG.md
index f5d77293..ef99487e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -18,6 +18,8 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 - Add macro attribute to `#[pyfn]` and `#[pyfunction]` to pass the module of a Python function to the function
   body. [#1143](https://github.com/PyO3/pyo3/pull/1143)
 - Add `add_function()` and `add_submodule()` functions to `PyModule` [#1143](https://github.com/PyO3/pyo3/pull/1143)
+- Add native `PyCFunction` and `PyFunction` types, change `add_function` to take a wrapper returning
+  a `&PyCFunction`instead of `PyObject`. [#1163](https://github.com/PyO3/pyo3/pull/1163)
 
 ### Changed
 - Exception types have been renamed from e.g. `RuntimeError` to `PyRuntimeError`, and are now only accessible by `&T` or `Py<T>` similar to other Python-native types. The old names continue to exist but are deprecated. [#1024](https://github.com/PyO3/pyo3/pull/1024)
diff --git a/README.md b/README.md
index ff041bf6..2e57a358 100644
--- a/README.md
+++ b/README.md
@@ -67,7 +67,7 @@ fn sum_as_string(a: usize, b: usize) -> PyResult<String> {
 /// A Python module implemented in Rust.
 #[pymodule]
 fn string_sum(py: Python, m: &PyModule) -> PyResult<()> {
-    m.add_function(wrap_pyfunction!(sum_as_string))?;
+    m.add_function(wrap_pyfunction!(sum_as_string, m)?)?;
 
     Ok(())
 }
diff --git a/examples/rustapi_module/src/datetime.rs b/examples/rustapi_module/src/datetime.rs
index 3ccb7c69..062dc958 100644
--- a/examples/rustapi_module/src/datetime.rs
+++ b/examples/rustapi_module/src/datetime.rs
@@ -215,29 +215,29 @@ impl TzClass {
 
 #[pymodule]
 fn datetime(_py: Python<'_>, m: &PyModule) -> PyResult<()> {
-    m.add_function(wrap_pyfunction!(make_date))?;
-    m.add_function(wrap_pyfunction!(get_date_tuple))?;
-    m.add_function(wrap_pyfunction!(date_from_timestamp))?;
-    m.add_function(wrap_pyfunction!(make_time))?;
-    m.add_function(wrap_pyfunction!(get_time_tuple))?;
-    m.add_function(wrap_pyfunction!(make_delta))?;
-    m.add_function(wrap_pyfunction!(get_delta_tuple))?;
-    m.add_function(wrap_pyfunction!(make_datetime))?;
-    m.add_function(wrap_pyfunction!(get_datetime_tuple))?;
-    m.add_function(wrap_pyfunction!(datetime_from_timestamp))?;
+    m.add_function(wrap_pyfunction!(make_date, m)?)?;
+    m.add_function(wrap_pyfunction!(get_date_tuple, m)?)?;
+    m.add_function(wrap_pyfunction!(date_from_timestamp, m)?)?;
+    m.add_function(wrap_pyfunction!(make_time, m)?)?;
+    m.add_function(wrap_pyfunction!(get_time_tuple, m)?)?;
+    m.add_function(wrap_pyfunction!(make_delta, m)?)?;
+    m.add_function(wrap_pyfunction!(get_delta_tuple, m)?)?;
+    m.add_function(wrap_pyfunction!(make_datetime, m)?)?;
+    m.add_function(wrap_pyfunction!(get_datetime_tuple, m)?)?;
+    m.add_function(wrap_pyfunction!(datetime_from_timestamp, m)?)?;
 
     // Python 3.6+ functions
     #[cfg(Py_3_6)]
     {
-        m.add_function(wrap_pyfunction!(time_with_fold))?;
+        m.add_function(wrap_pyfunction!(time_with_fold, m)?)?;
         #[cfg(not(PyPy))]
         {
-            m.add_function(wrap_pyfunction!(get_time_tuple_fold))?;
-            m.add_function(wrap_pyfunction!(get_datetime_tuple_fold))?;
+            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!(issue_219))?;
+    m.add_function(wrap_pyfunction!(issue_219, m)?)?;
     m.add_class::<TzClass>()?;
 
     Ok(())
diff --git a/examples/rustapi_module/src/othermod.rs b/examples/rustapi_module/src/othermod.rs
index b9955806..5c149d29 100644
--- a/examples/rustapi_module/src/othermod.rs
+++ b/examples/rustapi_module/src/othermod.rs
@@ -31,7 +31,7 @@ fn double(x: i32) -> i32 {
 
 #[pymodule]
 fn othermod(_py: Python<'_>, m: &PyModule) -> PyResult<()> {
-    m.add_function(wrap_pyfunction!(double))?;
+    m.add_function(wrap_pyfunction!(double, m)?)?;
 
     m.add_class::<ModClass>()?;
 
diff --git a/examples/word-count/src/lib.rs b/examples/word-count/src/lib.rs
index 50a00780..78213102 100644
--- a/examples/word-count/src/lib.rs
+++ b/examples/word-count/src/lib.rs
@@ -56,8 +56,8 @@ fn count_line(line: &str, needle: &str) -> usize {
 #[pymodule]
 fn word_count(_py: Python<'_>, m: &PyModule) -> PyResult<()> {
     m.add_wrapped(wrap_pyfunction!(search))?;
-    m.add_function(wrap_pyfunction!(search_sequential))?;
-    m.add_function(wrap_pyfunction!(search_sequential_allow_threads))?;
+    m.add_function(wrap_pyfunction!(search_sequential, m)?)?;
+    m.add_function(wrap_pyfunction!(search_sequential_allow_threads, m)?)?;
 
     Ok(())
 }
diff --git a/guide/src/function.md b/guide/src/function.md
index b33221c9..0e0277f3 100644
--- a/guide/src/function.md
+++ b/guide/src/function.md
@@ -36,7 +36,7 @@ fn double(x: usize) -> usize {
 
 #[pymodule]
 fn module_with_functions(py: Python, m: &PyModule) -> PyResult<()> {
-    m.add_function(wrap_pyfunction!(double)).unwrap();
+    m.add_function(wrap_pyfunction!(double, m)?).unwrap();
 
     Ok(())
 }
@@ -65,7 +65,7 @@ fn num_kwds(kwds: Option<&PyDict>) -> usize {
 
 #[pymodule]
 fn module_with_functions(py: Python, m: &PyModule) -> PyResult<()> {
-    m.add_function(wrap_pyfunction!(num_kwds)).unwrap();
+    m.add_function(wrap_pyfunction!(num_kwds, m)?).unwrap();
     Ok(())
 }
 
@@ -206,7 +206,7 @@ fn pyfunction_with_module(module: &PyModule) -> PyResult<&str> {
 
 #[pymodule]
 fn module_with_fn(py: Python, m: &PyModule) -> PyResult<()> {
-    m.add_function(wrap_pyfunction!(pyfunction_with_module))
+    m.add_function(wrap_pyfunction!(pyfunction_with_module, m)?)
 }
 
 # fn main() {}
diff --git a/guide/src/module.md b/guide/src/module.md
index 6b1d4581..aabba50b 100644
--- a/guide/src/module.md
+++ b/guide/src/module.md
@@ -73,7 +73,7 @@ fn subfunction() -> String {
 }
 
 fn init_submodule(module: &PyModule) -> PyResult<()> {
-    module.add_function(wrap_pyfunction!(subfunction))?;
+    module.add_function(wrap_pyfunction!(subfunction, module)?)?;
     Ok(())
 }
 
diff --git a/guide/src/trait_bounds.md b/guide/src/trait_bounds.md
index 65e173cd..f845b5c8 100644
--- a/guide/src/trait_bounds.md
+++ b/guide/src/trait_bounds.md
@@ -488,7 +488,7 @@ pub struct UserModel {
 #[pymodule]
 fn trait_exposure(_py: Python, m: &PyModule) -> PyResult<()> {
     m.add_class::<UserModel>()?;
-    m.add_function(wrap_pyfunction!(solve_wrapper))?;
+    m.add_function(wrap_pyfunction!(solve_wrapper, m)?)?;
     Ok(())
 }
 
diff --git a/pyo3-derive-backend/src/module.rs b/pyo3-derive-backend/src/module.rs
index a706100e..657d1134 100644
--- a/pyo3-derive-backend/src/module.rs
+++ b/pyo3-derive-backend/src/module.rs
@@ -44,7 +44,7 @@ pub fn process_functions_in_module(func: &mut syn::ItemFn) -> syn::Result<()> {
                 let item: syn::ItemFn = syn::parse_quote! {
                     fn block_wrapper() {
                         #function_to_python
-                        #module_name.add_function(&#function_wrapper_ident)?;
+                        #module_name.add_function(#function_wrapper_ident(#module_name)?)?;
                     }
                 };
                 stmts.extend(item.block.stmts.into_iter());
@@ -204,50 +204,26 @@ pub fn add_fn_to_module(
 
     let python_name = &spec.python_name;
 
-    let wrapper = function_c_wrapper(&func.sig.ident, &spec, pyfn_attrs.pass_module);
-
+    let name = &func.sig.ident;
+    let wrapper_ident = format_ident!("__pyo3_raw_{}", name);
+    let wrapper = function_c_wrapper(name, &wrapper_ident, &spec, pyfn_attrs.pass_module);
     Ok(quote! {
+        #wrapper
         fn #function_wrapper_ident<'a>(
-            args: impl Into<pyo3::derive_utils::WrapPyFunctionArguments<'a>>
-        ) -> pyo3::PyResult<pyo3::PyObject> {
-            let arg = args.into();
-            let (py, maybe_module) = arg.into_py_and_maybe_module();
-            #wrapper
-
-            let _def = pyo3::class::PyMethodDef {
-                ml_name: stringify!(#python_name),
-                ml_meth: pyo3::class::PyMethodType::PyCFunctionWithKeywords(__wrap),
-                ml_flags: pyo3::ffi::METH_VARARGS | pyo3::ffi::METH_KEYWORDS,
-                ml_doc: #doc,
-            };
-
-            let (mod_ptr, name) = if let Some(m) = maybe_module {
-                let mod_ptr = <pyo3::types::PyModule as ::pyo3::conversion::AsPyPointer>::as_ptr(m);
-                let name = m.name()?;
-                let name = <&str as pyo3::conversion::IntoPy<PyObject>>::into_py(name, py);
-                (mod_ptr, <PyObject as pyo3::AsPyPointer>::as_ptr(&name))
-            } else {
-                (std::ptr::null_mut(), std::ptr::null_mut())
-            };
-
-            let function = unsafe {
-                pyo3::PyObject::from_owned_ptr(
-                    py,
-                    pyo3::ffi::PyCFunction_NewEx(
-                        Box::into_raw(Box::new(_def.as_method_def())),
-                        mod_ptr,
-                        name
-                    )
-                )
-            };
-
-            Ok(function)
+            args: impl Into<pyo3::derive_utils::PyFunctionArguments<'a>>
+        ) -> pyo3::PyResult<&'a pyo3::types::PyCFunction> {
+            pyo3::types::PyCFunction::new_with_keywords(#wrapper_ident, stringify!(#python_name), #doc, args.into())
         }
     })
 }
 
 /// Generate static function wrapper (PyCFunction, PyCFunctionWithKeywords)
-fn function_c_wrapper(name: &Ident, spec: &method::FnSpec<'_>, pass_module: bool) -> TokenStream {
+fn function_c_wrapper(
+    name: &Ident,
+    wrapper_ident: &Ident,
+    spec: &method::FnSpec<'_>,
+    pass_module: bool,
+) -> TokenStream {
     let names: Vec<Ident> = get_arg_names(&spec);
     let cb;
     let slf_module;
@@ -265,9 +241,8 @@ fn function_c_wrapper(name: &Ident, spec: &method::FnSpec<'_>, pass_module: bool
         slf_module = None;
     };
     let body = pymethod::impl_arg_params(spec, None, cb);
-
     quote! {
-        unsafe extern "C" fn __wrap(
+        unsafe extern "C" fn #wrapper_ident(
             _slf: *mut pyo3::ffi::PyObject,
             _args: *mut pyo3::ffi::PyObject,
             _kwargs: *mut pyo3::ffi::PyObject) -> *mut pyo3::ffi::PyObject
diff --git a/src/derive_utils.rs b/src/derive_utils.rs
index cef90fd1..819599e9 100644
--- a/src/derive_utils.rs
+++ b/src/derive_utils.rs
@@ -209,17 +209,16 @@ where
 }
 
 /// Enum to abstract over the arguments of Python function wrappers.
-#[doc(hidden)]
-pub enum WrapPyFunctionArguments<'a> {
+pub enum PyFunctionArguments<'a> {
     Python(Python<'a>),
     PyModule(&'a PyModule),
 }
 
-impl<'a> WrapPyFunctionArguments<'a> {
+impl<'a> PyFunctionArguments<'a> {
     pub fn into_py_and_maybe_module(self) -> (Python<'a>, Option<&'a PyModule>) {
         match self {
-            WrapPyFunctionArguments::Python(py) => (py, None),
-            WrapPyFunctionArguments::PyModule(module) => {
+            PyFunctionArguments::Python(py) => (py, None),
+            PyFunctionArguments::PyModule(module) => {
                 let py = module.py();
                 (py, Some(module))
             }
@@ -227,14 +226,14 @@ impl<'a> WrapPyFunctionArguments<'a> {
     }
 }
 
-impl<'a> From<Python<'a>> for WrapPyFunctionArguments<'a> {
-    fn from(py: Python<'a>) -> WrapPyFunctionArguments<'a> {
-        WrapPyFunctionArguments::Python(py)
+impl<'a> From<Python<'a>> for PyFunctionArguments<'a> {
+    fn from(py: Python<'a>) -> PyFunctionArguments<'a> {
+        PyFunctionArguments::Python(py)
     }
 }
 
-impl<'a> From<&'a PyModule> for WrapPyFunctionArguments<'a> {
-    fn from(module: &'a PyModule) -> WrapPyFunctionArguments<'a> {
-        WrapPyFunctionArguments::PyModule(module)
+impl<'a> From<&'a PyModule> for PyFunctionArguments<'a> {
+    fn from(module: &'a PyModule) -> PyFunctionArguments<'a> {
+        PyFunctionArguments::PyModule(module)
     }
 }
diff --git a/src/ffi/funcobject.rs b/src/ffi/funcobject.rs
new file mode 100644
index 00000000..10b15345
--- /dev/null
+++ b/src/ffi/funcobject.rs
@@ -0,0 +1,34 @@
+use std::os::raw::c_int;
+
+use crate::ffi::object::{PyObject, PyTypeObject, Py_TYPE};
+
+#[cfg_attr(windows, link(name = "pythonXY"))]
+extern "C" {
+    #[cfg_attr(PyPy, link_name = "PyPyFunction_Type")]
+    pub static mut PyFunction_Type: PyTypeObject;
+}
+
+#[inline]
+pub unsafe fn PyFunction_Check(op: *mut PyObject) -> c_int {
+    (Py_TYPE(op) == &mut PyFunction_Type) as c_int
+}
+
+extern "C" {
+    pub fn PyFunction_NewWithQualName(
+        code: *mut PyObject,
+        globals: *mut PyObject,
+        qualname: *mut PyObject,
+    ) -> *mut PyObject;
+    pub fn PyFunction_New(code: *mut PyObject, globals: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_Code(op: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_GetGlobals(op: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_GetModule(op: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_GetDefaults(op: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_SetDefaults(op: *mut PyObject, defaults: *mut PyObject) -> c_int;
+    pub fn PyFunction_GetKwDefaults(op: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_SetKwDefaults(op: *mut PyObject, defaults: *mut PyObject) -> c_int;
+    pub fn PyFunction_GetClosure(op: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_SetClosure(op: *mut PyObject, closure: *mut PyObject) -> c_int;
+    pub fn PyFunction_GetAnnotations(op: *mut PyObject) -> *mut PyObject;
+    pub fn PyFunction_SetAnnotations(op: *mut PyObject, annotations: *mut PyObject) -> c_int;
+}
diff --git a/src/ffi/mod.rs b/src/ffi/mod.rs
index 3c5e9e94..4015b2cd 100644
--- a/src/ffi/mod.rs
+++ b/src/ffi/mod.rs
@@ -19,6 +19,7 @@ pub use self::eval::*;
 pub use self::fileobject::*;
 pub use self::floatobject::*;
 pub use self::frameobject::PyFrameObject;
+pub use self::funcobject::*;
 pub use self::genobject::*;
 pub use self::import::*;
 pub use self::intrcheck::*;
@@ -157,3 +158,5 @@ pub mod frameobject {
 
 pub(crate) mod datetime;
 pub(crate) mod marshal;
+
+pub(crate) mod funcobject;
diff --git a/src/lib.rs b/src/lib.rs
index 4c2313e3..2935c390 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -71,7 +71,7 @@
 //! #[pymodule]
 //! /// A Python module implemented in Rust.
 //! fn string_sum(py: Python, m: &PyModule) -> PyResult<()> {
-//!     m.add_function(wrap_pyfunction!(sum_as_string))?;
+//!     m.add_function(wrap_pyfunction!(sum_as_string, m)?)?;
 //!
 //!     Ok(())
 //! }
@@ -218,6 +218,20 @@ macro_rules! wrap_pyfunction {
     ($function_name: ident) => {{
         &pyo3::paste::expr! { [<__pyo3_get_function_ $function_name>] }
     }};
+
+    ($function_name: ident, $arg: expr) => {
+        pyo3::wrap_pyfunction!($function_name)(pyo3::derive_utils::PyFunctionArguments::from($arg))
+    };
+}
+
+/// Returns the function that is called in the C-FFI.
+///
+/// Use this together with `#[pyfunction]` and [types::PyCFunction].
+#[macro_export]
+macro_rules! raw_pycfunction {
+    ($function_name: ident) => {{
+        pyo3::paste::expr! { [<__pyo3_raw_ $function_name>] }
+    }};
 }
 
 /// Returns a function that takes a [Python] instance and returns a Python module.
diff --git a/src/python.rs b/src/python.rs
index 9b71ebf0..403737fe 100644
--- a/src/python.rs
+++ b/src/python.rs
@@ -134,7 +134,7 @@ impl<'p> Python<'p> {
     /// let gil = Python::acquire_gil();
     /// let py = gil.python();
     /// let m = PyModule::new(py, "pcount").unwrap();
-    /// m.add_function(wrap_pyfunction!(parallel_count)).unwrap();
+    /// m.add_function(wrap_pyfunction!(parallel_count, m).unwrap()).unwrap();
     /// let locals = [("pcount", m)].into_py_dict(py);
     /// py.run(r#"
     ///    s = ["Flow", "my", "tears", "the", "Policeman", "Said"]
diff --git a/src/types/function.rs b/src/types/function.rs
new file mode 100644
index 00000000..73aa04b7
--- /dev/null
+++ b/src/types/function.rs
@@ -0,0 +1,89 @@
+use std::ffi::{CStr, CString};
+
+use crate::derive_utils::PyFunctionArguments;
+use crate::exceptions::PyValueError;
+use crate::prelude::*;
+use crate::{class, ffi, AsPyPointer, PyMethodType};
+
+/// Represents a builtin Python function object.
+#[repr(transparent)]
+pub struct PyCFunction(PyAny);
+
+pyobject_native_var_type!(PyCFunction, ffi::PyCFunction_Type, ffi::PyCFunction_Check);
+
+impl PyCFunction {
+    /// Create a new built-in function with keywords.
+    pub fn new_with_keywords<'a>(
+        fun: ffi::PyCFunctionWithKeywords,
+        name: &str,
+        doc: &'static str,
+        py_or_module: PyFunctionArguments<'a>,
+    ) -> PyResult<&'a PyCFunction> {
+        let fun = PyMethodType::PyCFunctionWithKeywords(fun);
+        Self::new_(fun, name, doc, py_or_module)
+    }
+
+    /// Create a new built-in function without keywords.
+    pub fn new<'a>(
+        fun: ffi::PyCFunction,
+        name: &str,
+        doc: &'static str,
+        py_or_module: PyFunctionArguments<'a>,
+    ) -> PyResult<&'a PyCFunction> {
+        let fun = PyMethodType::PyCFunction(fun);
+        Self::new_(fun, name, doc, py_or_module)
+    }
+
+    fn new_<'a>(
+        fun: class::PyMethodType,
+        name: &str,
+        doc: &'static str,
+        py_or_module: PyFunctionArguments<'a>,
+    ) -> PyResult<&'a PyCFunction> {
+        let (py, module) = py_or_module.into_py_and_maybe_module();
+        let doc: &'static CStr = CStr::from_bytes_with_nul(doc.as_bytes())
+            .map_err(|_| PyValueError::py_err("docstring must end with NULL byte."))?;
+        let name = CString::new(name.as_bytes())
+            .map_err(|_| PyValueError::py_err("Function name cannot contain contain NULL byte."))?;
+        let def = match fun {
+            PyMethodType::PyCFunction(fun) => ffi::PyMethodDef {
+                ml_name: name.into_raw() as _,
+                ml_meth: Some(fun),
+                ml_flags: ffi::METH_VARARGS,
+                ml_doc: doc.as_ptr() as _,
+            },
+            PyMethodType::PyCFunctionWithKeywords(fun) => ffi::PyMethodDef {
+                ml_name: name.into_raw() as _,
+                ml_meth: Some(unsafe { std::mem::transmute(fun) }),
+                ml_flags: ffi::METH_VARARGS | ffi::METH_KEYWORDS,
+                ml_doc: doc.as_ptr() as _,
+            },
+            _ => {
+                return Err(PyValueError::py_err(
+                    "Only PyCFunction and PyCFunctionWithKeywords are valid.",
+                ))
+            }
+        };
+        let (mod_ptr, module_name) = if let Some(m) = module {
+            let mod_ptr = m.as_ptr();
+            let name = m.name()?.into_py(py);
+            (mod_ptr, name.as_ptr())
+        } else {
+            (std::ptr::null_mut(), std::ptr::null_mut())
+        };
+
+        unsafe {
+            py.from_owned_ptr_or_err::<PyCFunction>(ffi::PyCFunction_NewEx(
+                Box::into_raw(Box::new(def)),
+                mod_ptr,
+                module_name,
+            ))
+        }
+    }
+}
+
+/// Represents a Python function object.
+#[repr(transparent)]
+pub struct PyFunction(PyAny);
+
+pyobject_native_var_type!(PyFunction, ffi::PyFunction_Type, ffi::PyFunction_Check);
diff --git a/src/types/mod.rs b/src/types/mod.rs
index abdcdd00..b3915a8f 100644
--- a/src/types/mod.rs
+++ b/src/types/mod.rs
@@ -13,6 +13,7 @@ pub use self::datetime::{
 };
 pub use self::dict::{IntoPyDict, PyDict};
 pub use self::floatob::PyFloat;
+pub use self::function::{PyCFunction, PyFunction};
 pub use self::iterator::PyIterator;
 pub use self::list::PyList;
 pub use self::module::PyModule;
@@ -226,6 +227,7 @@ mod complex;
 mod datetime;
 mod dict;
 mod floatob;
+mod function;
 mod iterator;
 mod list;
 mod module;
diff --git a/src/types/module.rs b/src/types/module.rs
index b77a6fa4..baa343f6 100644
--- a/src/types/module.rs
+++ b/src/types/module.rs
@@ -9,8 +9,8 @@ use crate::ffi;
 use crate::instance::PyNativeType;
 use crate::pyclass::PyClass;
 use crate::type_object::PyTypeObject;
-use crate::types::PyTuple;
 use crate::types::{PyAny, PyDict, PyList};
+use crate::types::{PyCFunction, PyTuple};
 use crate::{AsPyPointer, IntoPy, Py, PyObject, Python};
 use std::ffi::{CStr, CString};
 use std::os::raw::c_char;
@@ -258,7 +258,7 @@ impl PyModule {
     /// }
     /// #[pymodule]
     /// fn double_mod(_py: Python, module: &PyModule) -> PyResult<()> {
-    ///     module.add_function(pyo3::wrap_pyfunction!(double))
+    ///     module.add_function(pyo3::wrap_pyfunction!(double, module)?)
     /// }
     /// ```
     ///
@@ -272,17 +272,11 @@ impl PyModule {
     /// }
     /// #[pymodule]
     /// fn double_mod(_py: Python, module: &PyModule) -> PyResult<()> {
-    ///     module.add("also_double", pyo3::wrap_pyfunction!(double)(module)?)
+    ///     module.add("also_double", pyo3::wrap_pyfunction!(double, module)?)
     /// }
     /// ```
-    pub fn add_function<'a>(
-        &'a self,
-        wrapper: &impl Fn(&'a Self) -> PyResult<PyObject>,
-    ) -> PyResult<()> {
-        let py = self.py();
-        let function = wrapper(self)?;
-        let name = function.getattr(py, "__name__")?;
-        let name = name.extract(py)?;
-        self.add(name, function)
+    pub fn add_function<'a>(&'a self, fun: &'a PyCFunction) -> PyResult<()> {
+        let name = fun.getattr("__name__")?.extract()?;
+        self.add(name, fun)
     }
 }
diff --git a/tests/test_module.rs b/tests/test_module.rs
index 7c278bdc..5ed75bf4 100644
--- a/tests/test_module.rs
+++ b/tests/test_module.rs
@@ -65,8 +65,8 @@ fn module_with_functions(_py: Python, m: &PyModule) -> PyResult<()> {
 
     m.add("foo", "bar").unwrap();
 
-    m.add_function(wrap_pyfunction!(double)).unwrap();
-    m.add("also_double", wrap_pyfunction!(double)(m)?).unwrap();
+    m.add_function(wrap_pyfunction!(double, m)?).unwrap();
+    m.add("also_double", wrap_pyfunction!(double, m)?).unwrap();
 
     Ok(())
 }
@@ -163,7 +163,7 @@ fn r#move() -> usize {
 fn raw_ident_module(_py: Python, module: &PyModule) -> PyResult<()> {
     use pyo3::wrap_pyfunction;
 
-    module.add_function(wrap_pyfunction!(r#move))
+    module.add_function(wrap_pyfunction!(r#move, module)?)
 }
 
 #[test]
@@ -188,7 +188,7 @@ fn custom_named_fn() -> usize {
 fn foobar_module(_py: Python, m: &PyModule) -> PyResult<()> {
     use pyo3::wrap_pyfunction;
 
-    m.add_function(wrap_pyfunction!(custom_named_fn))?;
+    m.add_function(wrap_pyfunction!(custom_named_fn, m)?)?;
     m.dict().set_item("yay", "me")?;
     Ok(())
 }
@@ -221,7 +221,7 @@ fn subfunction() -> String {
 fn submodule(module: &PyModule) -> PyResult<()> {
     use pyo3::wrap_pyfunction;
 
-    module.add_function(wrap_pyfunction!(subfunction))?;
+    module.add_function(wrap_pyfunction!(subfunction, module)?)?;
     Ok(())
 }
 
@@ -229,7 +229,7 @@ fn submodule(module: &PyModule) -> PyResult<()> {
 fn submodule_with_init_fn(_py: Python, module: &PyModule) -> PyResult<()> {
     use pyo3::wrap_pyfunction;
 
-    module.add_function(wrap_pyfunction!(subfunction))?;
+    module.add_function(wrap_pyfunction!(subfunction, module)?)?;
     Ok(())
 }
 
@@ -242,7 +242,7 @@ fn superfunction() -> String {
 fn supermodule(py: Python, module: &PyModule) -> PyResult<()> {
     use pyo3::wrap_pyfunction;
 
-    module.add_function(wrap_pyfunction!(superfunction))?;
+    module.add_function(wrap_pyfunction!(superfunction, module)?)?;
     let module_to_add = PyModule::new(py, "submodule")?;
     submodule(module_to_add)?;
     module.add_submodule(module_to_add)?;
@@ -291,7 +291,7 @@ fn vararg_module(_py: Python, m: &PyModule) -> PyResult<()> {
         ext_vararg_fn(py, a, vararg)
     }
 
-    m.add_function(pyo3::wrap_pyfunction!(ext_vararg_fn))
+    m.add_function(pyo3::wrap_pyfunction!(ext_vararg_fn, m)?)
         .unwrap();
     Ok(())
 }
@@ -368,15 +368,17 @@ fn pyfunction_with_module_and_args_kwargs<'a>(
 
 #[pymodule]
 fn module_with_functions_with_module(_py: Python, m: &PyModule) -> PyResult<()> {
-    m.add_function(pyo3::wrap_pyfunction!(pyfunction_with_module))?;
-    m.add_function(pyo3::wrap_pyfunction!(pyfunction_with_module_and_py))?;
-    m.add_function(pyo3::wrap_pyfunction!(pyfunction_with_module_and_arg))?;
+    m.add_function(pyo3::wrap_pyfunction!(pyfunction_with_module, m)?)?;
+    m.add_function(pyo3::wrap_pyfunction!(pyfunction_with_module_and_py, m)?)?;
+    m.add_function(pyo3::wrap_pyfunction!(pyfunction_with_module_and_arg, m)?)?;
     m.add_function(pyo3::wrap_pyfunction!(
-        pyfunction_with_module_and_default_arg
-    ))?;
+        pyfunction_with_module_and_default_arg,
+        m
+    )?)?;
     m.add_function(pyo3::wrap_pyfunction!(
-        pyfunction_with_module_and_args_kwargs
-    ))
+        pyfunction_with_module_and_args_kwargs,
+        m
+    )?)
 }
 
 #[test]
diff --git a/tests/test_pyfunction.rs b/tests/test_pyfunction.rs
index 0d8500a3..89b4dbd0 100644
--- a/tests/test_pyfunction.rs
+++ b/tests/test_pyfunction.rs
@@ -1,6 +1,7 @@
 use pyo3::buffer::PyBuffer;
 use pyo3::prelude::*;
-use pyo3::wrap_pyfunction;
+use pyo3::types::{PyCFunction, PyFunction};
+use pyo3::{raw_pycfunction, wrap_pyfunction};
 
 mod common;
 
@@ -62,3 +63,59 @@ assert a, array.array("i", [2, 4, 6, 8])
 "#
     );
 }
+
+#[pyfunction]
+fn function_with_pyfunction_arg(fun: &PyFunction) -> PyResult<&PyAny> {
+    fun.call((), None)
+}
+
+#[pyfunction]
+fn function_with_pycfunction_arg(fun: &PyCFunction) -> PyResult<&PyAny> {
+    fun.call((), None)
+}
+
+#[test]
+fn test_functions_with_function_args() {
+    let gil = Python::acquire_gil();
+    let py = gil.python();
+    let py_func_arg = wrap_pyfunction!(function_with_pyfunction_arg)(py).unwrap();
+    let py_cfunc_arg = wrap_pyfunction!(function_with_pycfunction_arg)(py).unwrap();
+    let bool_to_string = wrap_pyfunction!(optional_bool)(py).unwrap();
+
+    pyo3::py_run!(
+        py,
+        py_func_arg
+        py_cfunc_arg
+        bool_to_string,
+        r#"
+        def foo(): return "bar"
+        assert py_func_arg(foo) == "bar"
+        assert py_cfunc_arg(bool_to_string) == "Some(true)"
+        "#
+    )
+}
+
+#[test]
+fn test_raw_function() {
+    let gil = Python::acquire_gil();
+    let py = gil.python();
+    let raw_func = raw_pycfunction!(optional_bool);
+    let fun = PyCFunction::new_with_keywords(raw_func, "fun", "\0", py.into()).unwrap();
+    let res = fun.call((), None).unwrap().extract::<&str>().unwrap();
+    assert_eq!(res, "Some(true)");
+    let res = fun.call((false,), None).unwrap().extract::<&str>().unwrap();
+    assert_eq!(res, "Some(false)");
+    let no_module = fun.getattr("__module__").unwrap().is_none();
+    assert!(no_module);
+
+    let module = PyModule::new(py, "cool_module").unwrap();
+    module.add_function(fun).unwrap();
+    let res = module
+        .getattr("fun")
+        .unwrap()
+        .call((), None)
+        .unwrap()
+        .extract::<&str>()
+        .unwrap();
+    assert_eq!(res, "Some(true)");
+}