Py_AtExit():  Added brief note about the constraint on cleanup functions not
	      calling the Python API.
diff --git a/Doc/api/api.tex b/Doc/api/api.tex
index 4e1a850..26fc104 100644
--- a/Doc/api/api.tex
+++ b/Doc/api/api.tex
@@ -542,12 +542,15 @@
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{int}{Py_AtExit}{void (*func) ()}
-Register a cleanup function to be called by \code{Py_Finalize()}.  The
-cleanup function will be called with no arguments and should return no
-value.  At most 32 cleanup functions can be registered.  When the
-registration is successful, \code{Py_AtExit} returns 0; on failure, it
-returns -1.  The cleanup function registered last is called first.
-Each cleanup function will be called at most once.
+Register a cleanup function to be called by \cfunction{Py_Finalize()}.
+The cleanup function will be called with no arguments and should
+return no value.  At most 32 cleanup functions can be registered.
+When the registration is successful, \cfunction{Py_AtExit()} returns
+\code{0}; on failure, it returns \code{-1}.  The cleanup function
+registered last is called first.  Each cleanup function will be called
+at most once.  Since Python's internal finallization will have
+completed before the cleanup function, no Python APIs should be called
+by \var{func}.
 \end{cfuncdesc}