I guess the best solution right now will be to simply duplicate those
multi-megabyte databases with different sort orders, so that QuickSort does
not have to be called on the handheld.  The added storage requirements of
that solution are definitely easier to swallow than the painful sort
performance.

If you have a chance to point the right people at Access towards this issue,
that would be much appreciated.

That's one idea... the other idea is to instead do your own sort with
a separate index resource -- you keep the DB with the original order
and just sort a in-memory list of DB indices with the sort routine
doing the comparison using the actual records.  It's best to avoid
touching the original database but it just adds one level of
indirection to record access.

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