diff --git a/modules/juce_core/zip/juce_GZIPDecompressorInputStream.cpp b/modules/juce_core/zip/juce_GZIPDecompressorInputStream.cpp
index e351f883d2..71e0850727 100644
--- a/modules/juce_core/zip/juce_GZIPDecompressorInputStream.cpp
+++ b/modules/juce_core/zip/juce_GZIPDecompressorInputStream.cpp
@@ -90,7 +90,7 @@ namespace zlibNamespace
 class GZIPDecompressorInputStream::GZIPDecompressHelper
 {
 public:
-    GZIPDecompressHelper()
+    GZIPDecompressHelper (const bool dontWrap)
         : finished (true),
           needsDictionary (false),
           error (true),
@@ -100,7 +100,7 @@ public:
     {
         using namespace zlibNamespace;
         zerostruct (stream);
-        streamIsValid = (inflateInit2 (&stream, MAX_WBITS + 32 /* auto-detect gzip encoding */) == Z_OK);
+        streamIsValid = (inflateInit2 (&stream, dontWrap ? -MAX_WBITS : MAX_WBITS) == Z_OK);
         finished = error = ! streamIsValid;
     }
 
@@ -172,27 +172,30 @@ private:
 //==============================================================================
 GZIPDecompressorInputStream::GZIPDecompressorInputStream (InputStream* const source,
                                                           const bool deleteSourceWhenDestroyed,
-                                                          const int64 uncompressedLength)
+                                                          const bool noWrap_,
+                                                          const int64 uncompressedStreamLength_)
   : sourceStream (source, deleteSourceWhenDestroyed),
-    uncompressedStreamLength (uncompressedLength),
+    uncompressedStreamLength (uncompressedStreamLength_),
+    noWrap (noWrap_),
     isEof (false),
     activeBufferSize (0),
     originalSourcePos (source->getPosition()),
     currentPos (0),
     buffer ((size_t) GZIPDecompressHelper::gzipDecompBufferSize),
-    helper (new GZIPDecompressHelper())
+    helper (new GZIPDecompressHelper (noWrap_))
 {
 }
 
 GZIPDecompressorInputStream::GZIPDecompressorInputStream (InputStream& source)
   : sourceStream (&source, false),
     uncompressedStreamLength (-1),
+    noWrap (false),
     isEof (false),
     activeBufferSize (0),
     originalSourcePos (source.getPosition()),
     currentPos (0),
     buffer ((size_t) GZIPDecompressHelper::gzipDecompBufferSize),
-    helper (new GZIPDecompressHelper())
+    helper (new GZIPDecompressHelper (false))
 {
 }
 
@@ -275,7 +278,7 @@ bool GZIPDecompressorInputStream::setPosition (int64 newPos)
         isEof = false;
         activeBufferSize = 0;
         currentPos = 0;
-        helper = new GZIPDecompressHelper();
+        helper = new GZIPDecompressHelper (noWrap);
 
         sourceStream->setPosition (originalSourcePos);
     }
diff --git a/modules/juce_core/zip/juce_GZIPDecompressorInputStream.h b/modules/juce_core/zip/juce_GZIPDecompressorInputStream.h
index 26d9ac39fa..78a0b77b7f 100644
--- a/modules/juce_core/zip/juce_GZIPDecompressorInputStream.h
+++ b/modules/juce_core/zip/juce_GZIPDecompressorInputStream.h
@@ -57,6 +57,7 @@ public:
     */
     GZIPDecompressorInputStream (InputStream* sourceStream,
                                  bool deleteSourceWhenDestroyed,
+                                 bool noWrap = false,
                                  int64 uncompressedStreamLength = -1);
 
     /** Creates a decompressor stream.
@@ -79,7 +80,8 @@ public:
 private:
     //==============================================================================
     OptionalScopedPointer<InputStream> sourceStream;
-    int64 uncompressedStreamLength;
+    const int64 uncompressedStreamLength;
+    const bool noWrap;
     bool isEof;
     int activeBufferSize;
     int64 originalSourcePos, currentPos;
@@ -89,9 +91,6 @@ private:
     friend struct ContainerDeletePolicy<GZIPDecompressHelper>;
     ScopedPointer<GZIPDecompressHelper> helper;
 
-    // NB: The old 'noWrap' parameter is no longer needed in the constructor
-    JUCE_DEPRECATED (GZIPDecompressorInputStream (InputStream*, bool, bool));
-
     JUCE_DECLARE_NON_COPYABLE_WITH_LEAK_DETECTOR (GZIPDecompressorInputStream)
 };
 
diff --git a/modules/juce_core/zip/juce_ZipFile.cpp b/modules/juce_core/zip/juce_ZipFile.cpp
index febf391e1f..e0abb2d5f5 100644
--- a/modules/juce_core/zip/juce_ZipFile.cpp
+++ b/modules/juce_core/zip/juce_ZipFile.cpp
@@ -298,7 +298,7 @@ InputStream* ZipFile::createStreamForEntry (const int index)
 
         if (zei->compressed)
         {
-            stream = new GZIPDecompressorInputStream (stream, true, (int64) zei->entry.uncompressedSize);
+            stream = new GZIPDecompressorInputStream (stream, true, true, (int64) zei->entry.uncompressedSize);
 
             // (much faster to unzip in big blocks using a buffer..)
             stream = new BufferedInputStream (stream, 32768, true);