Proposed patch excludes the private API from the stable API. This includes:

_Py_Identifier-related API (other _Py_Identifier-related functions are already excluded):

struct _Py_Identifier;
#define _Py_static_string_init(value)
#define _Py_static_string(varname, value)
#define _Py_IDENTIFIER(varname)
PyAPI_FUNC(PyObject*) _PyUnicode_FromId(_Py_Identifier*);
PyAPI_FUNC(PyObject *) _PyObject_GetAttrId(PyObject *, struct _Py_Identifier *);
PyAPI_FUNC(int) _PyObject_SetAttrId(PyObject *, struct _Py_Identifier *, PyObject *);
PyAPI_FUNC(int) _PyObject_HasAttrId(PyObject *, struct _Py_Identifier *);
PyAPI_FUNC(PyObject *) _PyObject_CallMethodId(PyObject *o, _Py_Identifier *method, const char *format, ...);
PyAPI_FUNC(PyObject *) _PyObject_CallMethodId_SizeT(PyObject *o, _Py_Identifier *name, const char *format, ...);
PyAPI_FUNC(PyObject *) _PyObject_CallMethodIdObjArgs(PyObject *o, struct _Py_Identifier *method, ...);
PyAPI_FUNC(PyObject *) _PyDict_GetItemIdWithError(PyObject *dp, struct _Py_Identifier *key);
PyAPI_FUNC(PyObject *) _PyDict_GetItemId(PyObject *dp, struct _Py_Identifier *key);
PyAPI_FUNC(int) _PyDict_SetItemId(PyObject *dp, struct _Py_Identifier *key, PyObject *item);
PyAPI_FUNC(PyObject *) _PySys_GetObjectId(_Py_Identifier *key);

File helpers that hides OS-specific details and handle EINTR:

PyAPI_FUNC(PyObject *) _Py_device_encoding(int);
PyAPI_FUNC(FILE *) _Py_wfopen(const wchar_t *path, const wchar_t *mode);
PyAPI_FUNC(FILE*) _Py_fopen(const char *pathname, const char *mode);
PyAPI_FUNC(FILE*) _Py_fopen_obj(PyObject *path, const char *mode);
PyAPI_FUNC(Py_ssize_t) _Py_read(int fd, void *buf, size_t count);
PyAPI_FUNC(Py_ssize_t) _Py_write(int fd, const void *buf, size_t count);
PyAPI_FUNC(Py_ssize_t) _Py_write_noraise(int fd, const void *buf, size_t count);
PyAPI_FUNC(int) _Py_wreadlink(const wchar_t *path, wchar_t *buf, size_t bufsiz);
PyAPI_FUNC(wchar_t*) _Py_wrealpath(const wchar_t *path, wchar_t *resolved_path, size_t resolved_path_size);
PyAPI_FUNC(wchar_t*) _Py_wgetcwd(wchar_t *buf, size_t size);

Other OS functions:

PyAPI_FUNC(int) _PyOS_IsMainThread(void);
PyAPI_FUNC(void*) _PyOS_SigintEvent(void);
PyAPI_FUNC(int) _PyOS_GetOpt(int argc, wchar_t **argv, wchar_t *optstring);
PyAPI_FUNC(int) _PyOS_URandom(void *buffer, Py_ssize_t size);

Old helpers kept for binary compatibility of extensions built before 3.2.4:

PyAPI_FUNC(void) _PyTrash_deposit_object(PyObject*);
PyAPI_FUNC(void) _PyTrash_destroy_chain(void);
PyAPI_DATA(int) _PyTrash_delete_nesting;
PyAPI_DATA(PyObject *) _PyTrash_delete_later;

And other functions and data:

PyAPI_DATA(PyTypeObject) _PyNone_Type;
PyAPI_DATA(PyTypeObject) _PyNotImplemented_Type;
PyAPI_DATA(PyTypeObject) _PyMethodWrapper_Type;
PyAPI_DATA(int) _Py_SwappedOp[];

PyAPI_FUNC(Py_ssize_t) _Py_GetAllocatedBlocks(void);
PyAPI_FUNC(PyObject *) _PyObject_GC_Malloc(size_t size);
PyAPI_FUNC(PyObject *) _PyObject_GC_Calloc(size_t size);
PyAPI_FUNC(int) _PyObject_IsAbstract(PyObject *);

PyAPI_FUNC(PyObject*) _Py_strhex(const char* argbuf, const Py_ssize_t arglen);
PyAPI_FUNC(PyObject*) _Py_strhex_bytes(const char* argbuf, const Py_ssize_t arglen);

PyAPI_FUNC(void) _Py_add_one_to_index_F(int nd, Py_ssize_t *index, const Py_ssize_t *shape);
PyAPI_FUNC(void) _Py_add_one_to_index_C(int nd, Py_ssize_t *index, const Py_ssize_t *shape);

PyAPI_DATA(PyTypeObject) _PyNamespace_Type;
PyAPI_FUNC(PyObject *) _PyNamespace_New(PyObject *kwds);

PyAPI_FUNC(int) _PyOS_IsMainThread(void);
PyAPI_FUNC(void*) _PyOS_SigintEvent(void);
PyAPI_FUNC(int) _PyOS_GetOpt(int argc, wchar_t **argv, wchar_t *optstring);
PyAPI_FUNC(int) _PyOS_URandom(void *buffer, Py_ssize_t size);

PyAPI_FUNC(int) _PyState_AddModule(PyObject*, struct PyModuleDef*);
PyAPI_FUNC(PyThreadState *) _PyThreadState_Prealloc(PyInterpreterState *);
PyAPI_FUNC(void) _PyThreadState_Init(PyThreadState *);
PyAPI_FUNC(void) _PyThreadState_DeleteExcept(PyThreadState *tstate);
PyAPI_FUNC(void) _PyGILState_Reinit(void);
PyAPI_FUNC(PyThreadState *) _PyThreadState_UncheckedGet(void);

PyAPI_FUNC(void) _PyUnicode_ClearStaticStrings(void);
PyAPI_FUNC(int) _PyUnicode_EQ(PyObject *, PyObject *);

PyAPI_FUNC(void) _Py_DumpTraceback(int fd, PyThreadState *tstate);
PyAPI_FUNC(const char*) _Py_DumpTracebackThreads(int fd, PyInterpreterState *interp, PyThreadState *current_tstate);

PyAPI_FUNC(void) _PyImportZip_Init(void);

PyAPI_FUNC(PyObject *) _PyLong_GCD(PyObject *, PyObject *);

All these names are not documented (except _PyObject_GC_Calloc accidentally mentioned in What's New in 3.5) and are not used implicitly in macros (except _PyObject_CallMethodId_SizeT used in _PyObject_CallMethodId).

Many of these functions were added after implementing PEP 384 and changed its signature during its lifetime. They are not explicitly exclude from the stable API only by accident.

Added

PyAPI_FUNC(PyObject *) _PyObject_GenericGetAttrWithDict(PyObject *, PyObject *, PyObject *);
PyAPI_FUNC(int) _PyObject_GenericSetAttrWithDict(PyObject *, PyObject *, PyObject *, PyObject *);
PyAPI_FUNC(int) _Py_fstat(int fd, struct _Py_stat_struct *status);
PyAPI_FUNC(void) _PyEval_FiniThreads(void);

#23903 is closely related, but I haven't made it back to that one in some time.

New changeset d00f15af75ea by Serhiy Storchaka in branch 'default':
Issue #26900: Excluded underscored names and other private API from limited API.
https://hg.python.org/cpython/rev/d00f15af75ea

I didn't follow this discussion, but thanks for the fix Serhiy :-) By
the way, I started a thread on python-dev to discuss a new
organization of the C API for Python 3.7.

Maybe new private functions was added after writing the patch.

And many new public functions was added without guarding by specific Py_LIMITED_API value. This is separate issue.