How do I use GZipStream with System.IO.MemoryStream?

I am having an issue with this test function where I take an in memory string, compress it, and decompress it. The compression works great, but I can't seem to get the decompression to work.

//Compress
System.IO.MemoryStream outStream = new System.IO.MemoryStream();                
GZipStream tinyStream = new GZipStream(outStream, CompressionMode.Compress);
mStream.Position = 0;
mStream.CopyTo(tinyStream);

//Decompress    
outStream.Position = 0;
GZipStream bigStream = new GZipStream(outStream, CompressionMode.Decompress);
System.IO.MemoryStream bigStreamOut = new System.IO.MemoryStream();
bigStream.CopyTo(bigStreamOut);

//Results:
//bigStreamOut.Length == 0
//outStream.Position == the end of the stream.

I believe that bigStream out should at least have data in it, especially if my source stream (outStream) is being read. is this a MSFT bug or mine?