Solution - 1

Add following lines to your theme's functions.php file:

function my_clean_the_excerpts($excerpt) {
  $excerpt = strip_tags( $excerpt, '<p>' );
  return $excerpt;
}
add_filter('the_excerpt', 'my_clean_the_excerpts');

Solution - 2

Steven, can you please paste the code for that page? It seems you already have an excerpt filter in place in your functions.php. Also, please take a look at this plugin: http://wordpress.org/extend/plugins/advanced-excerpt/. I have it in my blog and it seems it does exactly what you wanted to achieve.