Allow Editor role to save custom options

I’m trying to create a custom admin page, which is no problem, however, I’d like to allow the editor role to save the custom options, and I’m getting the “Cheatin’ uh?” error. I have made the custom admin page available to the editors as follows:

add_action('admin_menu','my_options_menu');
function my_options_menu() {
  add_options_page('My Options', 'My Options', 'edit_others_posts', __FILE__, 'my_options_page');
}
function my_options_page() { ?>
  <form method='post' action='options.php'>
  ...etc...
  <?php settings_fields('my_options');
  </form>
<?php }

I think the reason that Editors are not able to save the options is because they don’t have “manage_options” capabilities, but I don’t know how to work around that, because I don’t want to give them that capability.

Can anyone help me through this?