I often use a solution more or less like this, that is based on a hash where the key is the value to be sorted (and in this case is case-insensitive) and the value is the actual string to be printed. It's quite compact and it kills dupes for free. As in this case I don't want it to kill dupes, I append an unique counter to the key so that each key is guaranteed to be unique.

Here's the code:

use strict;
my %hDat;
my $d; 
my $n;

map( ($hDat{lc $_ . $n++} = $_), <DATA> );
foreach $d (sort keys %hDat) { print $hDat{$d}; }

__DATA__
a
B
c
D
E
Aa
Xx
A
[download]

And here's the result:

a
A
Aa
B
c
D
E
Xx

You know, there is more than one way. :-)