Removing a constraint?

Does anyone know how to completely and accurately remove or drop a
constraint, specifically a foreign key constraint?  I tried to remove a
constraint by deleting it's trigger from pg_triggers.  This caused some
undesirable side effects with other tables involved with the constraint.  I
have several tables that I need to change the column constraints and
foreign key constraints on.  Recreating (drop and create) the table every
time I need to change a column constraint is a pain because all the objects
that reference the table would also need to be recreated (i.e. views and
triggers).  How do production DBAs successfully make changes to their
tables?

FYI, I was able to alter table add the same constraint many times.  Is this
a problem?  This created a new trigger in pg_triggers every time.