diff --git a/Doc/c-api/init.rst b/Doc/c-api/init.rst
index 58c79031de5..6b454131d87 100644
--- a/Doc/c-api/init.rst
+++ b/Doc/c-api/init.rst
@@ -396,9 +396,16 @@ Initializing and finalizing the interpreter
    :c:func:`Py_NewInterpreter` below) that were created and not yet destroyed since
    the last call to :c:func:`Py_Initialize`.  Ideally, this frees all memory
    allocated by the Python interpreter.  This is a no-op when called for a second
-   time (without calling :c:func:`Py_Initialize` again first).  Normally the
-   return value is ``0``.  If there were errors during finalization
-   (flushing buffered data), ``-1`` is returned.
+   time (without calling :c:func:`Py_Initialize` again first).
+
+   Since this is the reverse of :c:func:`Py_Initialize`, it should be called
+   in the same thread with the same interpreter active.  That means
+   the main thread and the main interpreter.
+   This should never be called while :c:func:`Py_RunMain` is running.
+
+   Normally the return value is ``0``.
+   If there were errors during finalization (flushing buffered data),
+   ``-1`` is returned.
 
    This function is provided for a number of reasons.  An embedding application
    might want to restart Python without having to restart the application itself.