diff --git a/CHANGELOG.md b/CHANGELOG.md
index 99b7959e0d0..8240d9ae7b4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -32,6 +32,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 - Remove FFI definition `PyCFunction_ClearFreeList` for Python 3.9 and later. [#1425](https://github.com/PyO3/pyo3/pull/1425)
 - `PYO3_CROSS_LIB_DIR` enviroment variable no long required when compiling for x86-64 Python from macOS arm64 and reverse. [#1428](https://github.com/PyO3/pyo3/pull/1428)
 - Fix FFI definition `_PyEval_RequestCodeExtraIndex` which took an argument of the wrong type. [#1429](https://github.com/PyO3/pyo3/pull/1429)
+- Fix FFI definition `PyIndex_Check` missing with the `abi3` feature. [#1436](https://github.com/PyO3/pyo3/pull/1436)
 
 ## [0.13.2] - 2021-02-12
 ### Packaging
diff --git a/src/ffi/objectabstract.rs b/src/ffi/abstract_.rs
similarity index 93%
rename from src/ffi/objectabstract.rs
rename to src/ffi/abstract_.rs
index c2403e1f526..e4ee4eadfe9 100644
--- a/src/ffi/objectabstract.rs
+++ b/src/ffi/abstract_.rs
@@ -51,6 +51,9 @@ extern "C" {
         ...
     ) -> *mut PyObject;
 
+    // skipped _PyObject_CallFunction_SizeT
+    // skipped _PyObject_CallMethod_SizeT
+
     #[cfg_attr(PyPy, link_name = "PyPyObject_CallFunctionObjArgs")]
     pub fn PyObject_CallFunctionObjArgs(callable: *mut PyObject, ...) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPyObject_CallMethodObjArgs")]
@@ -84,16 +87,30 @@ extern "C" {
     pub fn PyObject_Format(obj: *mut PyObject, format_spec: *mut PyObject) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPyObject_GetIter")]
     pub fn PyObject_GetIter(arg1: *mut PyObject) -> *mut PyObject;
+}
 
-    // PyIter_Check for unlimited API is in cpython/abstract_.rs
-    #[cfg(any(all(Py_LIMITED_API, Py_3_8), PyPy))]
-    #[cfg_attr(PyPy, link_name = "PyPyIter_Check")]
-    pub fn PyIter_Check(obj: *mut PyObject) -> c_int;
+// Defined as this macro in Python 3.6, 3.7 limited API, but relies on
+// non-limited PyTypeObject. Don't expose this since it cannot be used.
+#[cfg(not(any(Py_LIMITED_API, PyPy)))]
+#[inline]
+pub unsafe fn PyIter_Check(o: *mut PyObject) -> c_int {
+    (match (*crate::ffi::Py_TYPE(o)).tp_iternext {
+        Some(tp_iternext) => {
+            tp_iternext as *const std::os::raw::c_void
+                != crate::ffi::_PyObject_NextNotImplemented as _
+        }
+        None => false,
+    }) as c_int
 }
 
 extern "C" {
+    #[cfg(any(all(Py_3_8, Py_LIMITED_API), PyPy))]
+    #[cfg_attr(PyPy, link_name = "PyPyIter_Check")]
+    pub fn PyIter_Check(obj: *mut PyObject) -> c_int;
+
     #[cfg_attr(PyPy, link_name = "PyPyIter_Next")]
     pub fn PyIter_Next(arg1: *mut PyObject) -> *mut PyObject;
+    // skipped non-limited / 3.10 PyIter_Send
 
     #[cfg_attr(PyPy, link_name = "PyPyNumber_Check")]
     pub fn PyNumber_Check(o: *mut PyObject) -> c_int;
@@ -134,12 +151,10 @@ extern "C" {
     pub fn PyNumber_Xor(o1: *mut PyObject, o2: *mut PyObject) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPyNumber_Or")]
     pub fn PyNumber_Or(o1: *mut PyObject, o2: *mut PyObject) -> *mut PyObject;
-
-    #[cfg(PyPy)]
-    #[link_name = "PyPyIndex_Check"]
-    pub fn PyIndex_Check(o: *mut PyObject) -> c_int;
 }
 
+// Defined as this macro in Python 3.6, 3.7 limited API, but relies on
+// non-limited PyTypeObject. Don't expose this since it cannot be used.
 #[cfg(not(any(Py_LIMITED_API, PyPy)))]
 #[inline]
 pub unsafe fn PyIndex_Check(o: *mut PyObject) -> c_int {
@@ -148,6 +163,10 @@ pub unsafe fn PyIndex_Check(o: *mut PyObject) -> c_int {
 }
 
 extern "C" {
+    #[cfg(any(all(Py_3_8, Py_LIMITED_API), PyPy))]
+    #[link_name = "PyPyIndex_Check"]
+    pub fn PyIndex_Check(o: *mut PyObject) -> c_int;
+
     #[cfg_attr(PyPy, link_name = "PyPyNumber_Index")]
     pub fn PyNumber_Index(o: *mut PyObject) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPyNumber_AsSsize_t")]
@@ -232,7 +251,9 @@ extern "C" {
     pub fn PySequence_List(o: *mut PyObject) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPySequence_Fast")]
     pub fn PySequence_Fast(o: *mut PyObject, m: *const c_char) -> *mut PyObject;
-    // TODO: PySequence_Fast macros
+    // skipped PySequenc_Fast_GET_SIZE
+    // skipped PySequenc_Fast_GET_ITEM
+    // skipped PySequenc_Fast_GET_ITEMS
     pub fn PySequence_Count(o: *mut PyObject, value: *mut PyObject) -> Py_ssize_t;
     #[cfg_attr(PyPy, link_name = "PyPySequence_Contains")]
     pub fn PySequence_Contains(seq: *mut PyObject, ob: *mut PyObject) -> c_int;
diff --git a/src/ffi/cpython/abstract_.rs b/src/ffi/cpython/abstract_.rs
index 3dd33c49c94..b86ed1a7008 100644
--- a/src/ffi/cpython/abstract_.rs
+++ b/src/ffi/cpython/abstract_.rs
@@ -266,16 +266,11 @@ extern "C" {
     pub fn PyBuffer_Release(view: *mut Py_buffer);
 }
 
-#[inline]
-#[cfg(not(any(all(Py_3_8, Py_LIMITED_API), PyPy)))]
-pub unsafe fn PyIter_Check(o: *mut PyObject) -> c_int {
-    (match (*crate::ffi::Py_TYPE(o)).tp_iternext {
-        Some(tp_iternext) => {
-            tp_iternext as *const c_void != crate::ffi::_PyObject_NextNotImplemented as _
-        }
-        None => false,
-    }) as c_int
-}
+// PyIter_Check defined in ffi/abstract_.rs
+// PyIndex_Check defined in ffi/abstract_.rs
+// Not defined here because this file is not compiled under the
+// limited API, but the macros need to be defined for 3.6, 3.7 which
+// predate the limited API changes.
 
 // skipped PySequence_ITEM
 
diff --git a/src/ffi/mod.rs b/src/ffi/mod.rs
index 73fa2e3e547..bc739b681db 100644
--- a/src/ffi/mod.rs
+++ b/src/ffi/mod.rs
@@ -12,6 +12,7 @@ macro_rules! opaque_struct {
     };
 }
 
+pub use self::abstract_::*;
 pub use self::bltinmodule::*;
 pub use self::boolobject::*;
 pub use self::bytearrayobject::*;
@@ -47,7 +48,6 @@ pub use self::methodobject::*;
 pub use self::modsupport::*;
 pub use self::moduleobject::*;
 pub use self::object::*;
-pub use self::objectabstract::*; // FIXME: no matching objectabstract.h in cpython master
 pub use self::objimpl::*;
 pub use self::osmodule::*;
 pub use self::pyarena::*;
@@ -76,8 +76,7 @@ pub use self::weakrefobject::*;
 
 #[cfg(not(Py_LIMITED_API))]
 pub use self::cpython::*;
-
-// skipped abstract.h
+mod abstract_;
 // skipped asdl.h
 // skipped ast.h
 mod bltinmodule;
@@ -200,8 +199,6 @@ mod pythonrun; // TODO some functions need to be moved to pylifecycle
 mod osmodule;
 mod sysmodule; // TODO supports PEP-384 only; needs adjustment for Python 3.3 and 3.5
 
-mod objectabstract; // TODO supports PEP-384 only; needs adjustment for Python 3.3 and 3.5
-
 // mod pyctype; TODO excluded by PEP-384
 mod pystrtod; // TODO supports PEP-384 only; needs adjustment for Python 3.3 and 3.5
               // mod pystrcmp; TODO nothing interesting for Rust?
diff --git a/src/ffi/pyerrors.rs b/src/ffi/pyerrors.rs
index 4bd08d66d1d..f5b99fe1f2e 100644
--- a/src/ffi/pyerrors.rs
+++ b/src/ffi/pyerrors.rs
@@ -1,9 +1,5 @@
 use crate::ffi::object::*;
-#[cfg(PyPy)]
-use crate::ffi::objectabstract::PyObject_CallFunction;
 use crate::ffi::pyport::Py_ssize_t;
-#[cfg(PyPy)]
-use std::ffi::CStr;
 use std::os::raw::{c_char, c_int};
 
 #[repr(C)]
@@ -162,9 +158,11 @@ pub unsafe fn PyUnicodeDecodeError_Create(
     end: Py_ssize_t,
     _reason: *const c_char,
 ) -> *mut PyObject {
-    return PyObject_CallFunction(
+    return crate::ffi::PyObject_CallFunction(
         PyExc_UnicodeDecodeError,
-        CStr::from_bytes_with_nul(b"sy#nns\0").unwrap().as_ptr(),
+        std::ffi::CStr::from_bytes_with_nul(b"sy#nns\0")
+            .unwrap()
+            .as_ptr(),
         encoding,
         object,
         length,