lowercasing accented characters

[sewa]

Dear Monks, I'm expecting the following code to simply lowercase Ü (using Perl 5.8.8):

use strict;
use warnings;
use locale;
use POSIX qw(locale_h);                                               
+         
binmode( STDOUT, ":utf8" );                                           
+                                    
my $loc = setlocale(LC_CTYPE);
print "LC_CTYPE=$loc\n";                                              
+                                 
my $accented_char = "\x{00dc}"; #Upper case U with DIAERESIS
print "accented char=$accented_char\n";                               
+                                               
my $lowercased = lc( $accented_char );                                
+                                               
print "lowercased=$lowercased\n";

But it prints:

LC_CTYPE=en_US.UTF-8
accented char=Ü
lowercased=Ü

Based on perldoc for lc, I believe this should work, but it doesn't. Interestingly, accepting the input on stdin (with character encoding set to UTF-8 in the terminal) lowercases Ü correctly:

use strict;
use warnings;
use Encode;                                                           
+                    
binmode( STDIN,  ":utf8" );
binmode( STDOUT, ":utf8" );                                           
+                                                                     
+                                             
while( my $char = <> ) {
  chomp $char;
  my $lc_char = lc( $char );
  print "lowercased $char=$lc_char\n";
}

Any idea as to why the first script wouldn't work? Many thanks.