I'm unhappy with the solution I provided above because it seems like a really "Bad Idea" to close STDERR right in the middle of compilation, even if it is only for a little while. Who knows what other messages that is causing to be squelched! And that can make debugging a nightmare.

So I set out to find another more wholesome solution. It can't really be considered wholesome to tie a filehandle (tied filehandles aren't even yet fully reliable and fully implemented), but its better than sticking ones head in the sand like an ostrich by closing STDERR at such a critical moment.

So that's exactly my solution; tie STDERR to a class that squelches only messages containing the word "constant". Here it is, and as you can see, it works great.

use warnings;
use strict;

BEGIN{ 
    package ConstErr;
    use Tie::Handle;
    our @ISA = qw(Tie::Handle);
    sub TIEHANDLE {
        bless \my $i, shift;
    }
    sub PRINT {
        my $r = shift;
        print grep { $_ !~ m/constant/i } @_;
    }
    package main;
    tie *STDERR, 'ConstErr';
}

use constant PI => 3.14;
print PI, "\n";
use constant PI => 1000;
print PI, "\n";
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Again, let me reiterate that I still consider the whole idea to be a bad one, but if the purpose of this discussion is purely academic, and only seeking to find solutions to a theoretical problem, this is the best solution I can think of.