#process function does not receive pressed button name

I have a #process function that does something like:

function process($element, $edit)
{
   $element['#tree'] = TRUE;
   ...
   $element[0]['delete'] = array('#type' => 'button', '#value' =>
         t('Delete'));
   ...
   $element[1]['delete'] = array('#type' => 'button', '#value' =>
         t('Delete'));
   ...
   return $element;
}

Expected behavior:

$edit contains some kind of indication of which button was pressed (since using $_POST has been deprecated: http://drupal.org/node/64279#post_op)

Actual behavior:

$edit only contains the values of the other form elements