Alternate Tag for Header Image

Is there a way to dynamically access an ALT tag for a Header image? I am using a variation of the TwentyTen theme, and would like to get an alt tag into the IMG src without hard-coding one into header.php:

<img src="<?php header_image(); ?>" width="<?php echo HEADER_IMAGE_WIDTH; ?>" height="<?php echo HEADER_IMAGE_HEIGHT; ?>" alt="" />

Thanks for any help!