Someone mentioned to me that they couldn’t use PHP5-style object constructors when using the WP Widget API. I looked into it, and it turns out it does work. Example:

class My_Widget extends WP_Widget {
	function __construct() {
		$widget_ops = array( 'classname' => 'css-class', 'description' => 'Description' );
		parent::__construct( 'css-class', 'Title', $widget_ops );
	}
	// Rest of your widget subclass goes here
}

The key is using parent::__construct() instead of $this->WP_Widget().