You might also look into using CGI::Application. It uses "run modes" to sort out these issues.

Simplified Example (modified from CGI::App docs):

# In "WebApp.pm"...
package WebApp;
use base 'CGI::Application';
sub setup {
    my $self = shift;
    $self->mode_param('action');
    $self->run_modes(
        'delayedinv' => 'delayedinv',
        'del_inv' => 'del_inv',
        'played' => 'played'
        'stats' => 'stats'
        'AUTOLOAD' => 'defscreen'
    );
}

sub delayedinv { ... }
sub del_inv { ... }
sub payed { ... }
sub stats { ... }
sub defscreen { ... }

1;

### In "webapp.cgi"...
use WebApp;
my $webapp = WebApp->new();
$webapp->run();
[download]

It has many other nice features. See the docs for more info.