Create Table – multiple unique keys

I’m working on a plugin that creates a custom table. I’m trying to add a second UNIQUE KEY so the $wpdb->insert will fail if a duplicate value is specified.
dbDelta() has no problem with:

$sql = "CREATE TABLE " . $table_name . " (
     group_id int unsigned NOT NULL AUTO_INCREMENT,
     creation_date datetime DEFAULT '0000-00-00 00:00:00' NOT NULL,
     group_title tinytext NOT NULL,
     UNIQUE KEY  id (group_id)
     );";

But the table does not get added if I add a second UNIQUE KEY:

$sql = "CREATE TABLE " . $table_name . " (
     group_id int unsigned NOT NULL AUTO_INCREMENT,
     creation_date datetime DEFAULT '0000-00-00 00:00:00' NOT NULL,
     group_title tinytext NOT NULL,
     UNIQUE KEY  id (group_id),
     UNIQUE KEY  group (group_title)
     );";

What am I missing? Everything I’ve read says you can create multiple UNIQUE KEYs, but I can’t seem to get it working.

Thanks,
Ed