It's mentioned in Dr. Seuss's Oh the Places You'll Go: (just from memory, so pardon any errors) "So be your name Buxom or Bixby or Bray or MordecaiAllenVanAlli O'Shay . . . ." I like the nn Cai, but I don't see Mordecai being all that usable.
This is the first thing I thought of too. I'm a second grade teacher though so that could be why. I like the nickname Cai.