diff --git a/MagickCore/memory-private.h b/MagickCore/memory-private.h
index 0577a2f853..751d366d59 100644
--- a/MagickCore/memory-private.h
+++ b/MagickCore/memory-private.h
@@ -43,6 +43,20 @@ extern "C" {
 #define MagickAssumeAligned(address)  (address)
 #endif
 
+static inline size_t OverAllocateMemory(const size_t length)
+{
+  size_t
+    extent;
+
+  /*
+    Over allocate memory, typically used when concatentating strings.
+  */
+  extent=length;
+  if (extent < 131072)
+    for (extent=256; extent < length; extent*=2);
+  return(extent);
+}
+
 extern MagickPrivate void
   ResetMaxMemoryRequest(void),
   ResetVirtualAnonymousMemory(void);
diff --git a/MagickCore/string.c b/MagickCore/string.c
index 8e0e2e9379..dccef76a27 100644
--- a/MagickCore/string.c
+++ b/MagickCore/string.c
@@ -479,8 +479,8 @@ MagickExport MagickBooleanType ConcatenateString(
   length+=source_length;
   if (~length < MagickPathExtent)
     ThrowFatalException(ResourceLimitFatalError,"UnableToConcatenateString");
-  *destination=(char *) ResizeQuantumMemory(*destination,length+
-    MagickPathExtent,sizeof(**destination));
+  *destination=(char *) ResizeQuantumMemory(*destination,
+    OverAllocateMemory(length+MagickPathExtent),sizeof(**destination));
   if (*destination == (char *) NULL)
     ThrowFatalException(ResourceLimitFatalError,"UnableToConcatenateString");
   if (source_length != 0)
@@ -527,7 +527,19 @@ MagickExport void ConcatenateStringInfo(StringInfo *string_info,
   length=string_info->length;
   if (~length < source->length)
     ThrowFatalException(ResourceLimitFatalError,"UnableToConcatenateString");
-  SetStringInfoLength(string_info,length+source->length);
+  length+=source->length;
+  if (~length < MagickPathExtent)
+    ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
+  string_info->length=length;
+  if (string_info->datum == (unsigned char *) NULL)
+    string_info->datum=(unsigned char *) AcquireQuantumMemory(length+
+      MagickPathExtent,sizeof(*string_info->datum));
+  else
+    string_info->datum=(unsigned char *) ResizeQuantumMemory(
+      string_info->datum,OverAllocateMemory(length+MagickPathExtent),
+      sizeof(*string_info->datum));
+  if (string_info->datum == (unsigned char *) NULL)
+    ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
   (void) memcpy(string_info->datum+length,source->datum,source->length);
 }
 
@@ -2611,8 +2623,8 @@ MagickExport MagickBooleanType SubstituteString(char **string,
         */
         offset=(ssize_t) (p-(*string));
         extent=strlen(*string)+replace_extent-search_extent+1;
-        *string=(char *) ResizeQuantumMemory(*string,extent+MagickPathExtent,
-          sizeof(*p));
+        *string=(char *) ResizeQuantumMemory(*string,
+          OverAllocateMemory(extent+MagickPathExtent),sizeof(*p));
         if (*string == (char *) NULL)
           ThrowFatalException(ResourceLimitFatalError,"UnableToAcquireString");
         p=(*string)+offset;
diff --git a/coders/gif.c b/coders/gif.c
index 1301aa1df4..172fb34c8c 100644
--- a/coders/gif.c
+++ b/coders/gif.c
@@ -58,6 +58,7 @@
 #include "MagickCore/profile.h"
 #include "MagickCore/magick.h"
 #include "MagickCore/memory_.h"
+#include "MagickCore/memory-private.h"
 #include "MagickCore/monitor.h"
 #include "MagickCore/monitor-private.h"
 #include "MagickCore/option.h"
@@ -1102,8 +1103,9 @@ static Image *ReadGIFImage(const ImageInfo *image_info,ExceptionInfo *exception)
               if ((ssize_t) (count+offset+MagickPathExtent) >= (ssize_t) extent)
                 {
                   extent<<=1;
-                  comments=(char *) ResizeQuantumMemory(comments,extent+
-                    MagickPathExtent,sizeof(*comments));
+                  comments=(char *) ResizeQuantumMemory(comments,
+                    OverAllocateMemory(extent+MagickPathExtent),
+                    sizeof(*comments));
                   if (comments == (char *) NULL)
                     ThrowGIFException(ResourceLimitError,
                       "MemoryAllocationFailed");
diff --git a/coders/miff.c b/coders/miff.c
index 21b91d0889..eb6b755cd9 100644
--- a/coders/miff.c
+++ b/coders/miff.c
@@ -577,8 +577,8 @@ static Image *ReadMIFFImage(const ImageInfo *image_info,
               {
                 *p='\0';
                 length<<=1;
-                comment=(char *) ResizeQuantumMemory(comment,length+
-                  MagickPathExtent,sizeof(*comment));
+                comment=(char *) ResizeQuantumMemory(comment,
+                  OverAllocateMemory(length+MagickPathExtent),sizeof(*comment));
                 if (comment == (char *) NULL)
                   break;
                 p=comment+strlen(comment);