diff --git a/pep-0556.rst b/pep-0556.rst
index 971c54e01..e054763a2 100644
--- a/pep-0556.rst
+++ b/pep-0556.rst
@@ -143,7 +143,7 @@ An internal structure ``gc_mutex`` is added to avoid two GC runs at once:
 .. code-block::
 
    static struct {
-       PyThread_type_lock collecting;  /* taken when collecting */
+       PyThread_type_lock lock;  /* taken when collecting */
        PyThreadState *owner;  /* whichever thread is currently collecting
                                  (NULL if no collection is taking place) */
    } gc_mutex;
@@ -203,6 +203,9 @@ and live inside the ``gc`` module, unless otherwise noted:
 
 
    def lock_and_collect(generation=-1):
+       """
+       Perform a collection with thread safety.
+       """
        me = PyThreadState_GET()
        if gc_mutex.owner == me:
            # reentrant GC collection request, bail out
@@ -213,7 +216,7 @@ and live inside the ``gc`` module, unless otherwise noted:
        gc_mutex.owner = me
        try:
            if generation >= 0:
-               return collect_generation(generation)
+               return collect_with_callback(generation)
            else:
                return collect_generations()
        finally:
@@ -241,6 +244,9 @@ and live inside the ``gc`` module, unless otherwise noted:
 
 
    def PyGC_Malloc():
+       """
+       Allocate a GC-enabled object.
+       """
        # Update allocation statistics (same code as currently, omitted for brievity)
        if is_implicit_gc_desired():
            if gc_is_threaded:
@@ -308,7 +314,7 @@ and live inside the ``gc`` module, unless otherwise noted:
        Schedule collection of the given generation and wait for it to
        finish.
        """
-       return lock_and_collect(collection)
+       return lock_and_collect(generation)
 
 
 Discussion
@@ -328,7 +334,7 @@ for example if finalizers rely on some thread-local values.
 Explicit collections
 --------------------
 
-One may ask why explicit collections should not also be delegated to the
+One may ask whether explicit collections should also be delegated to the
 background thread.  The answer is it doesn't really matter: since
 ``gc.collect`` and ``PyGC_Collect`` actually *wait* for the collection to
 end (breaking this property would break compatibility), delegating the