diff --git a/Doc/api/init.tex b/Doc/api/init.tex
index ba96124..764c932 100644
--- a/Doc/api/init.tex
+++ b/Doc/api/init.tex
@@ -24,7 +24,7 @@
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{void}{Py_InitializeEx}{int initsigs}
-  This function works like \cfunction{Py_Initialize} if
+  This function works like \cfunction{Py_Initialize()} if
   \var{initsigs} is 1. If \var{initsigs} is 0, it skips
   initialization registration of signal handlers, which
   might be useful when Python is embedded. \versionadded{2.4}
@@ -517,14 +517,14 @@
   This is a common situation (most Python programs do not use
   threads), and the lock operations slow the interpreter down a bit.
   Therefore, the lock is not created initially.  This situation is
-  equivalent to having acquired the lock: when there is only a single
+  equivalent to having acquired the lock:  when there is only a single
   thread, all object accesses are safe.  Therefore, when this function
   initializes the lock, it also acquires it.  Before the Python
   \module{thread}\refbimodindex{thread} module creates a new thread,
   knowing that either it has the lock or the lock hasn't been created
   yet, it calls \cfunction{PyEval_InitThreads()}.  When this call
-  returns, it is guaranteed that the lock has been created and that it
-  has acquired it.
+  returns, it is guaranteed that the lock has been created and that the
+  calling thread has acquired it.
 
   It is \strong{not} safe to call this function when it is unknown
   which thread (if any) currently has the global interpreter lock.
@@ -533,6 +533,14 @@
   compile time.
 \end{cfuncdesc}
 
+\begin{cfuncdesc}{int}{PyEval_ThreadsInitialized}{}
+  Returns a non-zero value if \cfunction{PyEval_InitThreads()} has been
+  called.  This function can be called without holding the lock, and
+  therefore can be used to avoid calls to the locking API when running
+  single-threaded.  This function is not available when thread support
+  is disabled at compile time. \versionadded{2.4}
+\end{cfuncdesc}
+
 \begin{cfuncdesc}{void}{PyEval_AcquireLock}{}
   Acquire the global interpreter lock.  The lock must have been
   created earlier.  If this thread already has the lock, a deadlock