The JPEG spec defines two different "back end" modules for the final output
of compressed data: either Huffman coding or arithmetic coding is allowed.
The choice has no impact on image quality, but arithmetic coding usually
produces a smaller compressed file.  On typical images, arithmetic coding
produces a file 5 to 10 percent smaller than Huffman coding.  (All the
file-size numbers previously cited are for Huffman coding.)

Unfortunately, the particular variant of arithmetic coding specified by the
JPEG standard is subject to patents owned by IBM, AT&T, and Mitsubishi.
Thus *you cannot legally use JPEG arithmetic coding* unless you obtain
licenses from these companies.  (Patent law's "experimental use" exception
allows people to test a patented method in the context of scientific
research, but any commercial or routine personal use is infringement.)

I recommend that people not use JPEG arithmetic coding; the space savings
isn't great enough to justify the potential legal hassles.  In particular,
arithmetic coding *should not* be used for any images to be exchanged on
the Internet.  Even if you don't care about US patent law, other folks do.