Source: January 2005 ACBL Bulletin
After partner opens and your right-hand opponent overcalls 1NT, your only strong action is a penalty double. When your partner has shown some strength by opening the bidding, you may double a 1NT overcall for penalties with as few as 9 high-card points. If you have at least 9 Hcp, you know that your side has more than half the deck.
If you bid rather than double, partner will know that you have fewer than 9 HCP. Therefore you are welcome to bid (or even jump) with distributional hands. Any time you have good shape, defending 1NT should not be your first choice.
West North East South
1
1NT ?
You (South) hold:
J1096 
Q64 K4 
A752
Double and lead the J. You don’t have to worry about where your tricks are coming from. The key is that East has no chance to take seven tricks based on partner´s opening bid and your 10 HCP.
5 76 742 QJ109654
Preempt 3. Make them search for their major-suit fit(s) at the three level.
Q743 K742 4 K752
Pass. Your side may very well have a fit, but there is no way to find out. You are not obligated to respond with 8 HCP after an opponent’s notrump avercall.
Q8652 43 J1032 A7
Bid 2 . Your spades are too weak to bid. What if partner has a singleton? He almost certainly has four or more diamonds, so compete in your known fit.
KQ10976 43 8 6 853
Bid 2. You would be happy to play in 2 or push the opponents to the three level. Even if partner has only a singleton spade, your suit is strong enough to survive on its own.
53 J7542 9 AQ1097
Bid 2. Your clubs are excellent, but your hearts are not. Your non forcing bid may very well end the auction, so bid your stronger suit in case partner has to pass without a fit.
By the way: We all know players who incorrectly treat responder’s double as negative after a 1NT overcall. This is definitely not standard and is Alertable. I don’t recommend it, because a negative double should be played only after a natural overcall in a suit.
After an Overcall in a Suit
Partner opens the bidding and your right-hand opponent overcalls in a suit. What are your Options?
West North East South
1 1 ?
Pass: Often weak but may contain a hand with length and strength in spade. (trap pass) or a moderate hand with diamonds that’s not strong enough to bid 2.
Negative double: Shows at least four hearts and at least 6 high-card points (no upper limit). The double does not also promise diamonds.
1NT: 7-10 HCp, with one or more spade stoppers. 1NT denies four hearts because no negative double was made.
2: 6-10 points including distribution. At least four-card support for clubs, usually with fewer than four hearts (no negative double)
2: 10 or more HCP. Usually five or more diamonds, but four is possible. With long diamonds, the hand could include four hearts.
2 : 10 or more HCP and five or more hearts.
2: Cuebid showing a nice hand with good club support (preferably five cards). Some partnerships treat the cuebid as game-forcing; others do not. This bid denies four hearts, but says nothing about apades.
2NT: This jump shows a reasonable hand with at least one spade stopper. Some partnerships treat the bid as game forcing (13 or more HCP), while most agree that it is invitational (11-12 HCP). The bid denies four hearts.
3: Some partnerships treat this bid as a limit raise, inviting game. Raising opener’s minor would also deny four hearts (no negative double). Many experienced players define the jump raise in competition as a weak jump naise (WJR).
3, 3 : I strongly recommend that you play weak jump-shifts (W JS) in competition. Responder shows a very weak hand with a strong six or seven-card suit.
3NT: Shows two spade stoppers with enough strength to insist on game. Denies four hearts.
4 : Preemptive with an independent heart suit.
By the way#1: Nothing addressed in this list needs to be Alerted.
By the way #2: The most important issue for every partnership is that both players are in agreement as to what each bid or call shows.