diff --git a/src/exceptions.rs b/src/exceptions.rs
index 9bbb2e63..d55f74f1 100644
--- a/src/exceptions.rs
+++ b/src/exceptions.rs
@@ -12,8 +12,6 @@ use std::os::raw::c_char;
 #[macro_export]
 macro_rules! impl_exception_boilerplate {
     ($name: ident) => {
-        $crate::pyobject_native_type_fmt!($name);
-
         impl std::convert::From<&$name> for $crate::PyErr {
             fn from(err: &$name) -> $crate::PyErr {
                 $crate::PyErr::from_instance(err)
@@ -88,22 +86,10 @@ macro_rules! import_exception {
             $name,
             $crate::ffi::PyBaseExceptionObject,
             *$name::type_object_raw($crate::Python::assume_gil_acquired()),
-            Some(stringify!($module)),
-            $name::check
+            Some(stringify!($module))
         );
 
         impl $name {
-            /// Check if a python object is an instance of this exception.
-            ///
-            /// # Safety
-            /// `ptr` must be a valid pointer to a Python object
-            unsafe fn check(ptr: *mut $crate::ffi::PyObject) -> $crate::libc::c_int {
-                $crate::ffi::PyObject_TypeCheck(
-                    ptr,
-                    Self::type_object_raw($crate::Python::assume_gil_acquired()) as *mut _,
-                )
-            }
-
             fn type_object_raw(py: $crate::Python) -> *mut $crate::ffi::PyTypeObject {
                 use $crate::once_cell::GILOnceCell;
                 use $crate::AsPyPointer;
@@ -191,22 +177,10 @@ macro_rules! create_exception_type_object {
             $name,
             $crate::ffi::PyBaseExceptionObject,
             *$name::type_object_raw($crate::Python::assume_gil_acquired()),
-            Some(stringify!($module)),
-            $name::check
+            Some(stringify!($module))
         );
 
         impl $name {
-            /// Check if a python object is an instance of this exception.
-            ///
-            /// # Safety
-            /// `ptr` must be a valid pointer to a Python object
-            unsafe fn check(ptr: *mut $crate::ffi::PyObject) -> $crate::libc::c_int {
-                $crate::ffi::PyObject_TypeCheck(
-                    ptr,
-                    Self::type_object_raw($crate::Python::assume_gil_acquired()) as *mut _,
-                )
-            }
-
             fn type_object_raw(py: $crate::Python) -> *mut $crate::ffi::PyTypeObject {
                 use $crate::once_cell::GILOnceCell;
                 use $crate::AsPyPointer;
@@ -240,18 +214,7 @@ macro_rules! impl_native_exception (
         pub type $legacy_name = $crate::Py<$name>;
 
         $crate::impl_exception_boilerplate!($name);
-
-        impl $name {
-            /// Check if a python object is an instance of this exception.
-            ///
-            /// # Safety
-            /// `ptr` must be a valid pointer to a Python object
-            unsafe fn check(ptr: *mut $crate::ffi::PyObject) -> $crate::libc::c_int {
-                ffi::PyObject_TypeCheck(ptr, ffi::$exc_name as *mut _)
-            }
-        }
-
-        $crate::pyobject_native_type_core!($name, $layout, *(ffi::$exc_name as *mut ffi::PyTypeObject), Some("builtins"), $name::check);
+        $crate::pyobject_native_type_core!($name, $layout, *(ffi::$exc_name as *mut ffi::PyTypeObject), Some("builtins"));
     );
     ($name:ident, $legacy_name:ident, $exc_name:ident) => (
         impl_native_exception!($name, $legacy_name, $exc_name, ffi::PyBaseExceptionObject);
diff --git a/src/types/any.rs b/src/types/any.rs
index 5e8c2ff1..c50e7401 100644
--- a/src/types/any.rs
+++ b/src/types/any.rs
@@ -45,18 +45,10 @@ impl crate::AsPyPointer for PyAny {
     }
 }
 
-impl PartialEq for PyAny {
-    #[inline]
-    fn eq(&self, o: &PyAny) -> bool {
-        self.as_ptr() == o.as_ptr()
-    }
-}
-
-unsafe impl crate::PyNativeType for PyAny {}
 unsafe impl crate::type_object::PyLayout<PyAny> for ffi::PyObject {}
 impl crate::type_object::PySizedLayout<PyAny> for ffi::PyObject {}
 
-pyobject_native_type_convert!(
+pyobject_native_type_info!(
     PyAny,
     ffi::PyObject,
     ffi::PyBaseObject_Type,
@@ -66,7 +58,7 @@ pyobject_native_type_convert!(
 
 pyobject_native_type_extract!(PyAny);
 
-pyobject_native_type_fmt!(PyAny);
+pyobject_native_type_base!(PyAny);
 
 impl PyAny {
     /// Convert this PyAny to a concrete Python type.
diff --git a/src/types/iterator.rs b/src/types/iterator.rs
index ea0f2dc9..e9c0a674 100644
--- a/src/types/iterator.rs
+++ b/src/types/iterator.rs
@@ -24,7 +24,6 @@ use crate::{PyDowncastError, PyTryFrom};
 /// # Ok(())
 /// # }
 /// ```
-#[derive(Debug)]
 #[repr(transparent)]
 pub struct PyIterator(PyAny);
 pyobject_native_type_named!(PyIterator);
diff --git a/src/types/mod.rs b/src/types/mod.rs
index fbd01e41..9c5cae92 100644
--- a/src/types/mod.rs
+++ b/src/types/mod.rs
@@ -27,17 +27,65 @@ pub use self::string::{PyString, PyString as PyUnicode};
 pub use self::tuple::PyTuple;
 pub use self::typeobject::PyType;
 
+// Implementations core to all native types
+#[macro_export]
+macro_rules! pyobject_native_type_base(
+    ($name: ty $(,generics: <$($generics:ident),+>)?) => {
+        unsafe impl<$($($generics),+)?> $crate::PyNativeType for $name {}
+
+        impl<$($($generics),+)?> ::std::fmt::Debug for $name {
+            fn fmt(&self, f: &mut ::std::fmt::Formatter)
+                   -> Result<(), ::std::fmt::Error>
+            {
+                let s = self.repr().map_err(|_| ::std::fmt::Error)?;
+                f.write_str(&s.to_string_lossy())
+            }
+        }
+
+        impl<$($($generics),+)?> ::std::fmt::Display for $name {
+            fn fmt(&self, f: &mut ::std::fmt::Formatter)
+                   -> Result<(), ::std::fmt::Error>
+            {
+                let s = self.str().map_err(|_| ::std::fmt::Error)?;
+                f.write_str(&s.to_string_lossy())
+            }
+        }
+
+        impl<$($($generics),+)?> $crate::ToPyObject for $name
+        {
+            #[inline]
+            fn to_object(&self, py: $crate::Python) -> $crate::PyObject {
+                use $crate::AsPyPointer;
+                unsafe { $crate::PyObject::from_borrowed_ptr(py, self.as_ptr()) }
+            }
+        }
+
+        impl<$($($generics),+)?> PartialEq for $name {
+            #[inline]
+            fn eq(&self, o: &$name) -> bool {
+                use $crate::AsPyPointer;
+
+                self.as_ptr() == o.as_ptr()
+            }
+        }
+    };
+);
+
+// Implementations core to all native types except for PyAny (because they don't
+// make sense on PyAny / have different implementations).
 #[macro_export]
 macro_rules! pyobject_native_type_named (
-    ($name: ty $(,$type_param: ident)*) => {
-        impl<$($type_param,)*> ::std::convert::AsRef<$crate::PyAny> for $name {
+    ($name: ty $(,generics: <$($generics:ident),+>)?) => {
+        $crate::pyobject_native_type_base!($name $(,generics: <$($generics),+>)?);
+
+        impl<$($($generics),+)?> ::std::convert::AsRef<$crate::PyAny> for $name {
             #[inline]
             fn as_ref(&self) -> &$crate::PyAny {
                 &self.0
             }
         }
 
-        impl<$($type_param,)*> ::std::ops::Deref for $name {
+        impl<$($($generics),+)?> ::std::ops::Deref for $name {
             type Target = $crate::PyAny;
 
             #[inline]
@@ -46,9 +94,7 @@ macro_rules! pyobject_native_type_named (
             }
         }
 
-        unsafe impl<$($type_param,)*> $crate::PyNativeType for $name {}
-
-        impl<$($type_param,)*> $crate::AsPyPointer for $name {
+        impl<$($($generics),+)?> $crate::AsPyPointer for $name {
             /// Gets the underlying FFI pointer, returns a borrowed pointer.
             #[inline]
             fn as_ptr(&self) -> *mut $crate::ffi::PyObject {
@@ -56,43 +102,15 @@ macro_rules! pyobject_native_type_named (
             }
         }
 
-        impl<$($type_param,)*> PartialEq for $name {
-            #[inline]
-            fn eq(&self, o: &$name) -> bool {
-                use $crate::AsPyPointer;
-
-                self.as_ptr() == o.as_ptr()
-            }
-        }
-
-        impl<$($type_param,)*> $crate::IntoPy<$crate::Py<$name>> for &'_ $name {
+        impl<$($($generics),+)?> $crate::IntoPy<$crate::Py<$name>> for &'_ $name {
             #[inline]
             fn into_py(self, py: $crate::Python) -> $crate::Py<$name> {
                 use $crate::AsPyPointer;
                 unsafe { $crate::Py::from_borrowed_ptr(py, self.as_ptr()) }
             }
         }
-    };
-);
 
-#[macro_export]
-macro_rules! pyobject_native_type_core {
-    ($name: ty, $layout: path, $typeobject: expr, $module: expr, $checkfunction: path $(,$type_param: ident)*) => {
-        unsafe impl $crate::type_object::PyLayout<$name> for $layout {}
-        $crate::pyobject_native_type_named!($name $(,$type_param)*);
-        $crate::pyobject_native_type_convert!($name, $layout, $typeobject, $module, $checkfunction $(,$type_param)*);
-        $crate::pyobject_native_type_extract!($name $(,$type_param)*);
-
-        impl<'a, $($type_param,)*> ::std::convert::From<&'a $name> for &'a $crate::PyAny {
-            fn from(ob: &'a $name) -> Self {
-                unsafe{&*(ob as *const $name as *const $crate::PyAny)}
-            }
-        }
-
-
-        // TODO: Rust>=1.40 allows this impl for rust-numpy.
-        // So we should move this to `named` or `convert` when we bump MSRV.
-        impl<$($type_param,)*> From<&'_ $name> for $crate::Py<$name> {
+        impl<$($($generics),+)?> From<&'_ $name> for $crate::Py<$name> {
             #[inline]
             fn from(other: &$name) -> Self {
                 use $crate::AsPyPointer;
@@ -100,16 +118,32 @@ macro_rules! pyobject_native_type_core {
                 unsafe { $crate::Py::from_borrowed_ptr(other.py(), other.as_ptr()) }
             }
         }
+
+        impl<'a, $($($generics),+)?> ::std::convert::From<&'a $name> for &'a $crate::PyAny {
+            fn from(ob: &'a $name) -> Self {
+                unsafe{&*(ob as *const $name as *const $crate::PyAny)}
+            }
+        }
+    };
+);
+
+#[macro_export]
+macro_rules! pyobject_native_type_core {
+    ($name: ty, $layout: path, $typeobject: expr, $module: expr $(, $checkfunction:path)? $(,generics: <$($generics:ident),+>)? ) => {
+        unsafe impl $crate::type_object::PyLayout<$name> for $layout {}
+        $crate::pyobject_native_type_named!($name $(,generics: <$($generics),+>)?);
+        $crate::pyobject_native_type_info!($name, $layout, $typeobject, $module $(, $checkfunction)? $(,generics: <$($generics),+>)?);
+        $crate::pyobject_native_type_extract!($name $(,generics: <$($generics),+>)?);
     }
 }
 
 #[macro_export]
 macro_rules! pyobject_native_type_sized {
-    ($name: ty, $layout: path $(,$type_param: ident)*) => {
+    ($name: ty, $layout: path $(,generics: <$($generics:ident),+>)?) => {
         // To prevent inheriting native types with ABI3
         #[cfg(not(Py_LIMITED_API))]
         impl $crate::type_object::PySizedLayout<$name> for $layout {}
-        impl<'a, $($type_param,)*> $crate::derive_utils::PyBaseTypeUtils for $name {
+        impl<'a, $($($generics),+)?> $crate::derive_utils::PyBaseTypeUtils for $name {
             type Dict = $crate::pyclass_slots::PyClassDummySlot;
             type WeakRef = $crate::pyclass_slots::PyClassDummySlot;
             type LayoutAsBase = $crate::pycell::PyCellBase<$name>;
@@ -121,38 +155,36 @@ macro_rules! pyobject_native_type_sized {
 
 #[macro_export]
 macro_rules! pyobject_native_type {
-    ($name: ty, $layout: path, $typeobject: expr, $module: expr, $checkfunction: path $(,$type_param: ident)*) => {
-        $crate::pyobject_native_type_core!($name, $layout, $typeobject, $module, $checkfunction $(,$type_param)*);
-        $crate::pyobject_native_type_sized!($name, $layout $(,$type_param)*);
-        $crate::pyobject_native_type_fmt!($name $(,$type_param)*);
+    ($name: ty, $layout: path, $typeobject: expr, $module: expr, $checkfunction:path $(,generics: <$($generics:ident),+>)?) => {
+        $crate::pyobject_native_type_core!($name, $layout, $typeobject, $module, $checkfunction $(,generics: <$($generics),+>)?);
+        $crate::pyobject_native_type_sized!($name, $layout $(,generics: <$($generics),+>)?);
     };
-    ($name: ty, $layout: path, $typeobject: expr, $checkfunction: path $(,$type_param: ident)*) => {
+    ($name: ty, $layout: path, $typeobject: expr, $checkfunction:path $(,generics: <$($generics:ident),+>)?) => {
         $crate::pyobject_native_type! {
-            $name, $layout, $typeobject, Some("builtins"), $checkfunction $(,$type_param)*
+            $name, $layout, $typeobject, Some("builtins"), $checkfunction $(,generics: <$($generics),+>)?
         }
     };
 }
 
 #[macro_export]
 macro_rules! pyobject_native_var_type {
-    ($name: ty, $typeobject: expr, $module: expr, $checkfunction: path $(,$type_param: ident)*) => {
+    ($name: ty, $typeobject: expr, $module: expr, $checkfunction:path $(,generics: <$($generics:ident),+>)?) => {
         $crate::pyobject_native_type_core!(
-            $name, $crate::ffi::PyObject, $typeobject, Some("builtins"), $checkfunction $(,$type_param)*);
-        $crate::pyobject_native_type_fmt!($name $(,$type_param)*);
+            $name, $crate::ffi::PyObject, $typeobject, Some("builtins"), $checkfunction $(,generics: <$($generics),+>)?);
     };
-    ($name: ty, $typeobject: expr, $checkfunction: path $(,$type_param: ident)*) => {
+    ($name: ty, $typeobject: expr, $checkfunction: path $(,generics: <$($generics:ident),+>)?) => {
         $crate::pyobject_native_var_type! {
-            $name, $typeobject, Some("builtins"), $checkfunction $(,$type_param)*
+            $name, $typeobject, Some("builtins"), $checkfunction $(,generics: <$($generics),+>)?
         }
     };
 }
 
-// NOTE: This macro is not included in pyobject_native_type_convert!
+// NOTE: This macro is not included in pyobject_native_type_base!
 // because rust-numpy has a special implementation.
 #[macro_export]
 macro_rules! pyobject_native_type_extract {
-    ($name: ty $(,$type_param: ident)*) => {
-        impl<'py, $($type_param,)*> $crate::FromPyObject<'py> for &'py $name {
+    ($name: ty $(,generics: <$($generics:ident),+>)?) => {
+        impl<'py, $($($generics),+)?> $crate::FromPyObject<'py> for &'py $name {
             fn extract(obj: &'py $crate::PyAny) -> $crate::PyResult<Self> {
                 $crate::PyTryFrom::try_from(obj).map_err(Into::into)
             }
@@ -161,10 +193,10 @@ macro_rules! pyobject_native_type_extract {
 }
 
 #[macro_export]
-macro_rules! pyobject_native_type_convert(
+macro_rules! pyobject_native_type_info(
     ($name: ty, $layout: path, $typeobject: expr,
-     $module: expr, $checkfunction: path $(,$type_param: ident)*) => {
-        unsafe impl<$($type_param,)*> $crate::type_object::PyTypeInfo for $name {
+     $module: expr $(, $checkfunction:path)? $(,generics: <$($generics:ident),+>)?) => {
+        unsafe impl<$($($generics),+)?> $crate::type_object::PyTypeInfo for $name {
             type Type = ();
             type BaseType = $crate::PyAny;
             type Layout = $layout;
@@ -183,43 +215,13 @@ macro_rules! pyobject_native_type_convert(
                 unsafe { &mut $typeobject }
             }
 
-            #[allow(unused_unsafe)]
-            fn is_type_of(ptr: &$crate::PyAny) -> bool {
-                use $crate::AsPyPointer;
-                unsafe { $checkfunction(ptr.as_ptr()) > 0 }
-            }
-        }
-
-        impl<$($type_param,)*> $crate::ToPyObject for $name
-        {
-            #[inline]
-            fn to_object(&self, py: $crate::Python) -> $crate::PyObject {
-                use $crate::AsPyPointer;
-                unsafe { $crate::PyObject::from_borrowed_ptr(py, self.as_ptr()) }
-            }
-        }
-    };
-);
-
-#[macro_export]
-macro_rules! pyobject_native_type_fmt(
-    ($name: ty $(,$type_param: ident)*) => {
-        impl<$($type_param,)*> ::std::fmt::Debug for $name {
-            fn fmt(&self, f: &mut ::std::fmt::Formatter)
-                   -> Result<(), ::std::fmt::Error>
-            {
-                let s = self.repr().map_err(|_| ::std::fmt::Error)?;
-                f.write_str(&s.to_string_lossy())
-            }
-        }
-
-        impl<$($type_param,)*> ::std::fmt::Display for $name {
-            fn fmt(&self, f: &mut ::std::fmt::Formatter)
-                   -> Result<(), ::std::fmt::Error>
-            {
-                let s = self.str().map_err(|_| ::std::fmt::Error)?;
-                f.write_str(&s.to_string_lossy())
-            }
+            $(
+                fn is_type_of(ptr: &$crate::PyAny) -> bool {
+                    use $crate::AsPyPointer;
+                    #[allow(unused_unsafe)]
+                    unsafe { $checkfunction(ptr.as_ptr()) > 0 }
+                }
+            )?
         }
     };
 );