diff --git a/Misc/NEWS b/Misc/NEWS
index eeeaab0..cd44835 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -50,6 +50,8 @@
 Extension Modules
 -----------------
 
+- Issue #3116:  marshal.dumps() had quadratic behavior for strings > 32Mb.
+
 - Issue #2138: Add factorial() the math module.
 
 - The heapq module does comparisons using LT instead of LE.  This
diff --git a/Python/marshal.c b/Python/marshal.c
index 6db46e4..140192f 100644
--- a/Python/marshal.c
+++ b/Python/marshal.c
@@ -67,7 +67,7 @@
 	size = PyString_Size(p->str);
 	newsize = size + size + 1024;
 	if (newsize > 32*1024*1024) {
-		newsize = size + 1024*1024;
+		newsize = size + (size >> 3);	/* 12.5% overallocation */
 	}
 	if (_PyString_Resize(&p->str, newsize) != 0) {
 		p->ptr = p->end = NULL;