Defense vs. Doubles. Over a direct double, I've found that it's best to play systems on, with the following additional agreements. (1) If responder passes, opener is forced to redouble. Responder may either leave the redouble in for business (when the double was for penalty and responder has enough that he thinks 1NT will make), or initiate a scramble for a 4-3 fit on the 2-level by bidding his cheapest four-card suit. (2) If responder redoubles, opener must bid 2C. Responder can then pass or sign off in 2D.
The advantages of this system are that (1) since it doesn't give up any of the methods that would be available over a pass, it can be played over both penalty and non-penalty doubles, although responder's choice of action will of course be influenced by the meaning of the double, and (2) it allows responder to sign off in any suit at the 2-level, initiate a scramble, or play 1NT redoubled. When responder's suit is a minor, he also has a choice of signing off at the two level (by redoubling) or at the three level (via a minor-suit transfer). Finally, responder has the option of using Stayman, which may be useful if he holds a weak major two-suiter.
Over a balancing double, opener can't wait to see whether responder passes, so something has to give; balancing that, responder is known to hold neither substantial high-card strength nor major-suit length. If the double is for business, opener should bid a strong five-card minor if he has one. If opener passes and next hand also passes, responder may (1) sign off in his own 5-card minor, (2) redouble to ask partner to bid his cheapest 4-card suit, starting a runout, or (3) pass with a maximum and the expectation of making 1NT doubled.
Defense vs. Two-Level Suit Interference. Over a 2C bid that does not promise a real club suit, I play "systems on". Every bid means exactly what it would have meant otherwise, except that double is now Stayman. Over any other two-bid, double is penalty and Lebensohl applies. Direct (or "fast") denies. A cue-bid (direct or after Lebensohl) by responder is Stayman, asking partner to bid a 4-card major.
Defense vs. Higher-Level Interference. Double is penalty. Bidding shows a five-card suit and is forcing to game. A cue-bid of the enemy suit by responder is Stayman and shows a very strong hand, since the auction will potentially end up at a very high level. If opener rebids in NT after responder's cue-bid, it doesn't necessarily confirm a stopper in the enemy suit; it simply denies the ability to make any other bid.
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Defense vs. Doubles of Artificial Responses. If a Stayman 2C response is doubled, opener should make his normal response when holding a four-card major. With no four-card major, opener should (1) bid 2D with a five-card or strong four-card diamond suit, (2) redouble with five-card or strong four-card club suit, and (3) pass otherwise. If a transfer bid is doubled, opener normally pass the transfer back around to responder, who can then bid the suit himself, putting the doubler on lead. However, if opener was planning to superaccept, he should still do so (though he may choose to superaccept a major-suit transfer bid by bidding just 2M rather than 3M). Also, if opener wasn't planning to superaccept, but has a strong holding in the suit doubled, he should redouble.
Defense vs. Overcalls of Responder's Bid. All doubles are for penalty. If opener takes a bid when responder may have a minimum, he shows a maximum, a hand unsuitable for penalizing the opponents' contract, and a solid bid.