Hiding empty custom fields

I have defined a custom post type, and with it, a number of custom fields that are displayed. All is well, except, I cannot hide fields, when they are not filled in. This is how I tried to do it:

function the_brb_meta() {
    global $id;

    if ( $keys = get_post_custom_keys() ) {
        foreach ( $keys as $key ) {
            $keyt = trim($key);
            if ( '_' == $keyt{0} )
                continue;
                echo "<ul class=\"post-meta\">\n";
                   $values = array_map('trim', get_post_custom_values($key));
                $value = implode($values,', ');
                if(!empty($key)) {
                       echo "<li><span class=\"post-meta-key\">$key:</span> $value</li>\n";
                    echo "</ul>\n";
                    }
            }
    }
}

but the empty fields still show up. What is wrong with my code’s logic?

Any help appreciated.