With a run of 100,000, randomizing the alphabet, the distribution was mostly even, with a slight bias of items at the front of the list tending to wind up after the mid-point and items at the rear tending to wind up before the mid-point. For the 100,000 runs, the first item's average position was 1 past the mid-point, while the last item's average position was 1 before the mid-point. But this is close enough to a perfect shuffle for most uses.

my @lList = (1..10);
my ($lPos, $lRand);
# For every position in the list, swap it with a random
# position earlier in the list.
foreach $lPos (1..$#list) {
  $lRand = int(rand($lPos));
  @lList[$lPos, $lRand] = @lList[$lRand, $lPos];
}
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To correct the bias, use the following code:

my @lList = (1..10);
my ($lPos, $lRand);
# For every position in the list, swap it with a random
# position earlier in the list.
foreach $lPos (1..$#list) {
  $lRand = int(rand($lPos+1));
  @lList[$lPos, $lRand] = @lList[$lRand, $lPos];
}
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