diff --git a/Misc/NEWS b/Misc/NEWS
index 6363f80..cdc3f9c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -48,6 +48,8 @@
 Library
 -------
 
+- Issue #3116 and #1792:  Fix quadratic behavior in marshal.dumps().
+
 - Issue #2682: ctypes callback functions no longer contain a cyclic
   reference to themselves.
 
diff --git a/Python/marshal.c b/Python/marshal.c
index 897c15e..c305bbe 100644
--- a/Python/marshal.c
+++ b/Python/marshal.c
@@ -65,7 +65,10 @@
 	if (p->str == NULL)
 		return; /* An error already occurred */
 	size = PyString_Size(p->str);
-	newsize = size + 1024;
+	newsize = size + size + 1024;
+	if (newsize > 32*1024*1024) {
+		newsize = size + (size >> 3);	/* 12.5% overallocation */
+	}
 	if (_PyString_Resize(&p->str, newsize) != 0) {
 		p->ptr = p->end = NULL;
 	}