I set up the buffer_bytes_max to correspond with a buffer size of 4 kB. For S16_LE and stereo interleaved, that means 1024 frames in the buffer.  When it goes above 512, I get a BUG warning from ALSA:

[ 241.219184] ALSA sound/core/pcm_lib.c:352 BUG: pcmC3D0p:0, pos = 512, buffer size = 512, period size = 128

I guess I will have to drill down into ALSA and see where that buffer size is coming from.

-Paul Stone