There is one way that you can overcome it. It's pretty bad, though. :/

#!/usr/bin/perl -l

package Example::Module;

use overload '""' => sub { ref shift };

sub new {
    bless [ $_[1] || "default" ], shift;
}

sub Example::Module {
    return Example::Module::->new(@_);
}

sub print_it {
    print $_[0]->[0];
}

package main;

$a = Example::Module();
$a->print_it;

$b = Example::Module("b");
$b->print_it;
__END__
default
b
[download]

Yeah. Not very pretty, I know. Also, it breaks if no parameters is an illegal option (i.e. your constructor returns undef or dies). This would come into play for calls such as Example::Module->print_it. Of course in that case you may as well just return "Example::Module" as the original code had.