diff --git a/Misc/NEWS b/Misc/NEWS
index 874f27bc041..acedeb1d4b6 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -13,6 +13,8 @@ What's New in Python 3.0 release candiate 3?
 Core and Builtins
 -----------------
 
+- Issue #3327: Don't overallocate in the modules_by_index list.
+
 - Issue #1721812:  Binary set operations and copy() returned the input type
   instead of the appropriate base type.  This was incorrect because set 
   subclasses would be created without their __init__() method being called.
diff --git a/Python/pystate.c b/Python/pystate.c
index 2a9b7443f97..fe5de5f4d22 100644
--- a/Python/pystate.c
+++ b/Python/pystate.c
@@ -234,7 +234,7 @@ _PyState_AddModule(PyObject* module, struct PyModuleDef* def)
 	if (!def)
 		return -1;
 	if (!state->modules_by_index) {
-		state->modules_by_index = PyList_New(20);
+		state->modules_by_index = PyList_New(0);
 		if (!state->modules_by_index)
 			return -1;
 	}