Refactor the main routine to handle both cases and give it a "utility" sounding name, then make the other two routines wrappers with a nicer interface into the big daddy.

sub big_daddy{ my ($self,$type,@args)=@_; ... }
sub foo{ my $self=shift; $self->big_daddy('FOO',@_); }
sub bar{ my $self=shift; $self->big_daddy('BAR',@_); }
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If you really feel like being evil, you could make $type come from caller() so that the behaviour of bigdaddy is determined by what has called it, but IMO this is nasty stuff that isnt worth bothering with.