Cascading Trigger - changing row on delete does not delete row

All,

I have 2 tables which both have triggers on them.  When I delete a row
on table A, a cascading trigger ends up modifying rows in table B.  The
modified rows in table B trigger an update on rows in table A which
happens to be the same row that I am trying to delete.

I don't get any errors from the delete, yet PostgreSQL tells me 0 rows
affected by the delete and sure enough the row I just tried to delete is
still there.  Running the delete a 2nd time works because the trigger
does not cascade and effect the deleted row.

Is there a way to know that a row I am deleting is being deleted so I
don't update it?

I thought about adding a boolean column 'is_being_deleted' but I can't
set that to true without updating the row (which I'm trying to avoid).

I've thought about using PL/Perl to access transaction-level global
variables where I could store the ID of the row I'm deleting and fetch
that value in order to avoid it in my updates ... but I don't want
invoke the PL/Perl interpreter and slow down what I'm already doing in
PL/PGSQL.  Are there transaction-level variables in PL/PGSQL (globals)?

Suggestions?

-- Dante