GZipStream and DeflateStream produce bigger files

I'm trying to use deflate/gzip streams in C# but it appears that the files after compression are bigger than before.

For example, I compress a docx file of 900ko, but it produce a 1.4Mo one !

And it does it for every file I tried.

May be I am wrong in the way I'm doing it? Here is my code :

  FileStream input = File.OpenRead(Environment.CurrentDirectory + "/file.docx");
  FileStream output = File.OpenWrite(Environment.CurrentDirectory + "/compressedfile.dat");

  GZipStream comp = new GZipStream(output, CompressionMode.Compress);

  while (input.Position != input.Length)
      comp.WriteByte((byte)input.ReadByte());

  input.Close();

  comp.Close(); // automatically call flush at closing
  output.Close();