Limit a Wordpress query to a specific category?

I use this code to pull in a random post in my WordPress sidebar. The code below works fine, but I'd like to limit it to a specific category id.

Any ideas?

$rand_posts = $wpdb->get_results("SELECT * FROM $wpdb->posts WHERE post_type = 'post' AND post_status = 'publish' ORDER BY RAND() LIMIT 1");

Code (markup):

 

Found it. Just in case anyone else needs an answer to this...

$rand_posts = get_posts('numberposts=1&category=4&orderby=rand');
foreach ($rand_posts as $post) {
the_title();
// etc
}

PHP:

EDIT, actually... found an even better way:

$my_query = new WP_Query('showposts=1&category_name='.$catslug.'&orderby=rand'); 
while ($my_query->have_posts()) {
$my_query->the_post();
the_title();
// etc
}

PHP: