Problems with Cached DBI connections

[Simon Wistow]

Has anybody else seen a phenomenom where they're using cached DBI 
connections but N processes run out of connections despite the fact that 
the DB (in this case MySQL - not sure if that's relevant) has a 
connection limit of M where N<M?

FWIW "show processlist" shows that there are indeed M connections coming 
in but I'm not sure where from.

Ideas? Workarounds? Fact of life?