diff --git a/Doc/c-api/code.rst b/Doc/c-api/code.rst
index 6932bb1..57e8072 100644
--- a/Doc/c-api/code.rst
+++ b/Doc/c-api/code.rst
@@ -31,11 +31,11 @@
 
    Return true if *co* is a :class:`code` object
 
-.. c:function:: int PyCode_GetNumFree(PyObject *co)
+.. c:function:: int PyCode_GetNumFree(PyCodeObject *co)
 
    Return the number of free variables in *co*.
 
-.. c:function:: PyCodeObject *PyCode_New(int argcount, int kwonlyargcount, int nlocals, int stacksize, int flags, PyObject *code, PyObject *consts, PyObject *names, PyObject *varnames, PyObject *freevars, PyObject *cellvars, PyObject *filename, PyObject *name, int firstlineno, PyObject *lnotab)
+.. c:function:: PyCodeObject* PyCode_New(int argcount, int kwonlyargcount, int nlocals, int stacksize, int flags, PyObject *code, PyObject *consts, PyObject *names, PyObject *varnames, PyObject *freevars, PyObject *cellvars, PyObject *filename, PyObject *name, int firstlineno, PyObject *lnotab)
 
    Return a new code object.  If you need a dummy code object to
    create a frame, use :c:func:`PyCode_NewEmpty` instead.  Calling
@@ -43,7 +43,7 @@
    version since the definition of the bytecode changes often.
 
 
-.. c:function:: int PyCode_NewEmpty(const char *filename, const char *funcname, int firstlineno)
+.. c:function:: PyCodeObject* PyCode_NewEmpty(const char *filename, const char *funcname, int firstlineno)
 
    Return a new empty code object with the specified filename,
    function name, and first line number.  It is illegal to
diff --git a/Doc/c-api/conversion.rst b/Doc/c-api/conversion.rst
index dfc0a3a..9578f98 100644
--- a/Doc/c-api/conversion.rst
+++ b/Doc/c-api/conversion.rst
@@ -119,13 +119,13 @@
    .. versionadded:: 3.1
 
 
-.. c:function:: char* PyOS_stricmp(char *s1, char *s2)
+.. c:function:: int PyOS_stricmp(char *s1, char *s2)
 
    Case insensitive comparison of strings. The function works almost
    identically to :c:func:`strcmp` except that it ignores the case.
 
 
-.. c:function:: char* PyOS_strnicmp(char *s1, char *s2, Py_ssize_t  size)
+.. c:function:: int PyOS_strnicmp(char *s1, char *s2, Py_ssize_t  size)
 
    Case insensitive comparison of strings. The function works almost
    identically to :c:func:`strncmp` except that it ignores the case.
diff --git a/Doc/c-api/init.rst b/Doc/c-api/init.rst
index 7507e3b..95ff4ee 100644
--- a/Doc/c-api/init.rst
+++ b/Doc/c-api/init.rst
@@ -646,7 +646,7 @@
    :c:func:`PyGILState_Release` on the same thread.
 
 
-.. c:function:: PyThreadState PyGILState_GetThisThreadState()
+.. c:function:: PyThreadState* PyGILState_GetThisThreadState()
 
    Get the current thread state for this thread.  May return ``NULL`` if no
    GILState API has been used on the current thread.  Note that the main thread
diff --git a/Doc/c-api/type.rst b/Doc/c-api/type.rst
index ce39e4d..6f9c7a8 100644
--- a/Doc/c-api/type.rst
+++ b/Doc/c-api/type.rst
@@ -51,13 +51,13 @@
    modification of the attributes or base classes of the type.
 
 
-.. c:function:: int PyType_HasFeature(PyObject *o, int feature)
+.. c:function:: int PyType_HasFeature(PyTypeObject *o, int feature)
 
    Return true if the type object *o* sets the feature *feature*.  Type features
    are denoted by single bit flags.
 
 
-.. c:function:: int PyType_IS_GC(PyObject *o)
+.. c:function:: int PyType_IS_GC(PyTypeObject *o)
 
    Return true if the type object includes support for the cycle detector; this
    tests the type flag :const:`Py_TPFLAGS_HAVE_GC`.
diff --git a/Doc/c-api/unicode.rst b/Doc/c-api/unicode.rst
index a74a73d..fb7ba67 100644
--- a/Doc/c-api/unicode.rst
+++ b/Doc/c-api/unicode.rst
@@ -1615,7 +1615,7 @@
    ISO-8859-1 if it contains non-ASCII characters".
 
 
-.. c:function:: int PyUnicode_RichCompare(PyObject *left,  PyObject *right,  int op)
+.. c:function:: PyObject* PyUnicode_RichCompare(PyObject *left,  PyObject *right,  int op)
 
    Rich compare two unicode strings and return one of the following:
 
diff --git a/Doc/c-api/veryhigh.rst b/Doc/c-api/veryhigh.rst
index 41cdd6b..499eb3e 100644
--- a/Doc/c-api/veryhigh.rst
+++ b/Doc/c-api/veryhigh.rst
@@ -95,12 +95,6 @@
    leaving *closeit* set to ``0`` and *flags* set to *NULL*.
 
 
-.. c:function:: int PyRun_SimpleFileFlags(FILE *fp, const char *filename, PyCompilerFlags *flags)
-
-   This is a simplified interface to :c:func:`PyRun_SimpleFileExFlags` below,
-   leaving *closeit* set to ``0``.
-
-
 .. c:function:: int PyRun_SimpleFileEx(FILE *fp, const char *filename, int closeit)
 
    This is a simplified interface to :c:func:`PyRun_SimpleFileExFlags` below,