use strict;
use warnings;

my $xml = join '', <DATA>;
while ($xml =~ s/(<\/?.*?>)\s+(<\/?.*?>)/$1$2/sg) {}
print $xml;

__DATA__
<outermost>
    <innermost>
        <first>1</first>
        <second/>
        <third>These spaces are to be preserved.</third>
    </innermost>
</outermost>