[Bridge Crew] Dynamic Dice Pools

I now have a much better space for this game, and several others I'm working on, at http://uk.groups.yahoo.com/group/jigsawesome/

Yesterday, I got to playtest Bridge Crew for the first time with a group of brave volunteers (they were doubly-brave, since they had just finished playtesting another game of mine!) and we used the system outlined above.

Once issue that cropped up though was the bidding for the Captain's Order: as one player pointed out, he had nothing to lose by bidding as low as possible straight away! If he bid low, then no-one else could underbid him, so he was guaranteed to be able to carry out the order and the worst outcome that would happen is that the Alien player would gain that die... which wouldn't be very high anyway!

So, how can I give players an incentive to gamble for higher dice? What could be changed, added or removed that would make players think twice about going straight to the lowest bid in order to secure themselves a chance to win a die?

There is also a related issue to this, in that the lowest bid possible is "With respect, Sir..." which secures you the Order, but the Captain does not give you a die; instead, you have to gamble one from your Officer Pool. This makes sense tactically if you adopt a Hostile or Friendly attitude, since you could still get end up ahead (Friendly: you get to swap dice; Hostile: Winner takes all dice used) or just secure your place in the Captain's seat. The problem we experienced was that players kept undercutting each other by bidding "With respect, Sir..." so the Encounter Pool was being drained much faster than the Commission Pool and the Captain's Order was rarely being followed!

OK, that's two issues, but they are linked: what can be done to encourage players not to make the lowest bid possible?