One of your toughest competitive bidding problems comes when the opponents make a two-suited overcall. Unusual 2NT overcalls and Michaels cuebids can work like preempts because they use up bidding space you may need to find your contract. They can also cause problems because there's no "Standard American" way for responder to show many types of hands.
The old-fashioned approach to dealing with these overcalls was to use cuebids of the opponent's suits to show stoppers or controls. After 1 by partner, 2NT by RHO (clubs and diamonds), your 3 cuebid would show a diamond stopper and ask partner to bid 3NT with a club stopper. Much more valuable, though, are systems that describe your holdings in suits the over-caller doesn't have.
Today, many partnerships play the Unusual vs. Unusual convention, which uses the cuebids to show length in your two potential trump suits. The name refers to the "unusual" meaning of responder's cuebids after an opponent's unusual 2NT overcall, but the treatment can be used over some Michaels cuebids, too. Actually, this convention isn't so unusual. You'll see it listed in the lower right-hand corner of many pairs' convention cards, and you may even have it on yours. But because there are different ways to play Unusual vs. Unusual, just adding it to your card doesn't constitute a clear agreement. You and your partner need to discuss which form of the convention you'll use and agree on the exact meanings of responder's bids.
One form of Unusual vs. Unusual uses the lower-ranking cuebid to promise support for partner's suit and the higher-ranking cuebid to show length in the unbid suit.
A slightly different treatment -- and the one that's probably most popular among expert players -- follows the same principle, but ties the cuebids to the rank of the suits. This easy-to-remember system, often called "Lower-Lower", works like this: "Lower-Lower" responses over the opponents' Unusual 2NT When an opponent overcalls 2NT, you assume that the two suits he showed are "theirs" and the other two suits (the suit partner opened and the unbid suit) are "yours". As responder, you have two cuebids available in their suits to describe your length in your suits. The meanings of your cuebids are:
Using this system, if partner opens a major and the opponent overcalls 2NT, your 3 cuebid always shows hearts; a 3 cuebid always shows spades. The length and strength you need for these cuebids depend on whether you're raising partner or showing the unbid suit.
Cuebids operate the same way when partner opens a minor. After 1 by partner, 2NT by LHO (diamonds and hearts),
The only variation occurs when partner opens a minor and the opponent's 2NT overcall shows both minors. In this rare case, use 3 and 3 as cuebids to describe 4+-card length in the majors.
After 1 by partner, 2NT on your right (clubs and diamonds)
Other responses
Because these cuebids handle several types of hands, they allow you to better define your other bids. After an opening bid by partner and a 2NT overcall, the meanings of your other responses are:
Try the Unusual vs. Unusual system with the following hands:
Partner RHO You 1 - 2NT? (Unusual clubs and diamonds)
1) A873 J1093 10732 2
2) J864 3 AJ92 KJ103
3) AQ85 KJ97 106 543
4) AQ1053 94 AJ K942
5) KQ10854 64 K3 765
6) AJ10 K10743 5 A753
Bid 4. You could also bid 3 (showing a limit-raise or better), then follow with a cuebid to show the forcing raise. The immediate splinter bid, though, is more descriptive and will help partner better evaluate his hand for a possible slam.
Another variation
If you want to play in 3NT you must double first then either double what the opponents run to or then bid 3NT.