Keeping background transparency when converting to GIF

Hello,

I'm having a tough time keeping transparency intact when using 
imagegif() on a transparent image.

The image is definitely transparent, as evidenced when using the PNG 
format .. but once I imagegif() it, the background takes on my 
transparent color, minus the transparency.

Is there something different I could do to make this work as desired?

Thanks!
-Jason Young

Brief example:

<?php
$font = 'verdana.ttf';

$im = imagecreatetruecolor(100, 50);
imagesavealpha($im, true);

$trans = imagecolorallocatealpha($im, 20, 50, 50, 127); // To 
demonstrate non-transparent color
$black = imagecolorallocate($im, 0, 0, 0);

imagefill($im, 0, 0, $trans);

imagettftext($im, 10, 0, 20, 20, $black, $font, 'A transparent 
background?');

//header('Content-Type: image/png');
// imagepng($im); // This works as expected.

header('Content-Type: image/gif');
imagegif($im); // This does not.

imagedestroy($im);
?>