I am far away from being a mighty Perl hacker, but I've done recursion depth counting this way all the time. It's "cleaner" because you don't have to understand Perl-specific techniques. And it's thread-safe, too? Cool ;) Didn't know that... But why keep the curly brackets?

sub recurse {
    my ($depth) = @_;
    print +("   .") x $depth . "current depth:$depth\n" ;
    recurse($depth + 1) if $depth < 3;
    print +("   .") x $depth . "current depth:$depth\n" ;
}

recurse(-1);
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This is the same, right? Additionally, I would start with recurse(0);