Recently, I received a zipx file with JPEG pictures, which were compressed using method 96. Method 96 is applied by WinZip 12.0 or newer on JPEG pictures when the best compression method is selected. The file had a compression ratio of 80.4%. The method 96 is well described here:

I tried the following programs to unzip the file:

Ubuntu 12.04 package Command Result
unzip unzip pictures.zipx Failed: "unsupported compression method 96"
p7zip-full 7z x pictures.zipx Failed: "Unsupported Method"
unar unar pictures.zipx Succeeded

Unar seemed to be the only unziping program for Linux capable of extracing zipx files made with compression method 96. It was not easy to find, because unar's main focus is the MacOS. More information is available at its homepage: