Teeny tiny Lezyne for me, but I only use it to start a little air in the tube before using a CO2 cartridge, and also as a theoretical backup in case I run out of CO2. I haven't had to pump up a tire all the way with it yet, but I think it would do the job.

Oh, and mounting it under the bottle cage is a good idea. I crashed with one in my jersey pocket, and it left a very painful bruise tattoo above my right hip...