When using constants with debugging, I'm usually using an environment variable to signal the level of debugging info required, with variations on the following code:

BEGIN {
    my $level = $ENV{'FOO_DEBUG'} || 0;
    eval "*Foo::DEBUG = sub () {$1}" if $level =~ m#^(\d+)$#s;
} #BEGIN

if (Foo::DEBUG) {
    print "We're debugging\n";
}
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sub BEGIN {
    my $level = $ENV{'FOO_DEBUG'} || 0;
    eval "*Foo::DEBUG = sub () {$1}" if $level =~ /^(\d+)$/s;
}
'???';
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sub BEGIN {
    my $level = $ENV{'FOO_DEBUG'} || 0;
    eval "*Foo::DEBUG = sub () {$1}" if $level =~ /^(\d+)$/s;
}
do {
    print "We're debugging\n"
};
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Hope this helps.

Liz