From the CB:

In my case I may not need to sort the entire list. I need to get the most recent file, then I may need the next most recent file, and perhaps the next one after that.

If most of the time, the latest satisfies your need, you could do a linear search for it. Then do something more expensive a real sort if you need further info.

my $newest_time;
my @newest_files;

my %times;
foreach my $file (@files) {
   my $time = (stat($file))[9];
   $times{$file} = $time;
   if ($time > $newest_time) {
      $newest_time = $time;
      @newest_files = $file;
   }
   elsif ($time == $newest_time) {
      push @newest_files, $file;
   }
}

foreach my $file (@newest_files) {
   if ( ...[ this is the file we want ]... ) {
      return $file;
   }
}

@files = sort { $times{$b} <=> $times{$a} } @files;

# Remove the ones we already checked.
splice(@files, 0, scalar(@newest_files));

foreach my $file (@files) {
   if ( ...[ this is the file we want ]... ) {
      return $file;
   }
}
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You might want to benchmark against sorting the whole list.

my %times;
$times{$_} = (stat($file))[9]
   foreach @files;
@files = sort { $times{$b} <=> $times{$a} } @files;
[download]

Update: Fixed problems raised by shmem.