Searchable Tweets

I am now successfully importing my bloggers Tweets into Drupal, and they can be viewed, and browsed and even sorted, they cannot however, be searched as they are not nodes. I can understand that Tweets cannot be indexed along with the node content of the site, and actually that wouldn't be my preferred way to do this anyway, but I would love an included function that allowed searching the Twitter table for Tweets that include my supplied text. I understand FeedAPI would create nodes from my tweets, but it doesn't provide the integration your module provides so I would have to run both and keep duplicate copies of Tweets in your table and the Node table. Not so good. Any ideas on how to make Tweets searchable?