diff --git a/Doc/api/init.tex b/Doc/api/init.tex
index 9225f69..e380bdb 100644
--- a/Doc/api/init.tex
+++ b/Doc/api/init.tex
@@ -696,15 +696,15 @@
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{int}{PyThreadState_SetAsyncExc}{long id, PyObject *exc}
-  Asynchronously raise an exception in a thread. 
+  Asynchronously raise an exception in a thread.
   The \var{id} argument is the thread id of the target thread;
   \var{exc} is the exception object to be raised.
   This function does not steal any references to \var{exc}.
-  To prevent naive misuse, you must write your own C extension 
-  to call this.  Must be called with the GIL held. 
-  Returns the number of thread states modified; if it returns a number 
-  greater than one, you're in trouble, and you should call it again 
-  with \var{exc} set to \constant{NULL} to revert the effect.
+  To prevent naive misuse, you must write your own C extension
+  to call this.  Must be called with the GIL held.
+  Returns the number of thread states modified; this is normally one, but
+  will be zero if the thread id isn't found.  If \var{exc} is
+  \constant{NULL}, the pending exception (if any) for the thread is cleared.
   This raises no exceptions.
   \versionadded{2.3}
 \end{cfuncdesc}