Thanks to all who offered advice. I may have been taking the book
definition of mediawait too literally -- as pertaining to removable
volumes, not disk.

I was able to correlate the MediaWait condition showed by TSMManager
with dsmaccnt.log records for the nodes last night.  20 nodes were
affected between 2:30 and 3:45 AM. None, the rest of the night.  And,
none the rest of the month except for one other night.

The Maximum Size Threshold on the pool, is set to No Limit.  So, I
believe biggee files are ruled out.

Finishing one backup and housekeeping cycle before the next one begins
is like sweeping sand back into the ocean.  We are always eager to
learn of a better broom.

I'll redefine smaller, more plentiful TSM volumes for this pool, and
see if that keeps the sand out of my socks.

With my thanks and best wishes,
Keith Arbogast