Order by field containing aggregate function result (MIN)

Hi, I'm having trouble with sorting during pagination. I'm trying to list users with lowest solvetime, but order key in paginate method doesn't seem to like order field if it's a result of aggregate function like MIN().

This is my action:

public function index() {   
        $this->paginate = array(
            'fields' => array('*, MIN(Game.time AS mintime'),
            'conditions' => array('Game.time IS NOT NULL AND Game.visible = 1 AND Game.end_time IS NOT NULL AND Game.moves IS NOT NULL'),
            'order' => array('mintime' => 'ASC'),
            'group' => array('Game.uid'),
            'limit' => 3
        );
        $games = $this->paginate('Game');

        $this->set('games', $games);
    }

...it doesn't even add an ORDER BY clause in the debug. If some other field is set as order argument it works.

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