Alternative solution is to copy what GZIPOutputStream does

GZIPOutputStream.java

  public GZIPOutputStream(OutputStream out, int size, boolean syncFlush)
      throws IOException
  {
      super(out, new Deflater(Deflater.DEFAULT_COMPRESSION, true),
            size,
            syncFlush);
      usesDefaultDeflater = true;
      writeHeader();
      crc.reset();
  }