I have just further modified the compression stuff in AFNI to use pigz and pbzip2 by default in place of gzip and bzip2, if the former programs are present. AFNI pipes the data through these external programs -- it doesn't actually do the compression or decompression internally using library code.
AFNi doesn't supply pigz or pbzip2, but I recommend that users install these programs (if not already present in your path). They are much faster than the original versions when you have a multi-core computer.