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The Lebensohl Convention
The auction begins 1NT from partner and next hand overcalls 2H and you hold
(a)     xx        or  (b)    Kx
         xx                      xx
         KJxxxx              AQxxxx
         Axx                   Axx

With (a) you wish to play in 3D (given that the opponents will let you) and on (b) you want to be in game.
If your agreement is to play  a 3D bid as non-forcing then a cue-bid (3H) is your only option with (b) and here’s hoping you land on your feet. However if 3D is forcing then you must go quietly with hand (a) and perhaps sell out to the heart partscore. I am willing to bet that some of you don’t have an agreement and make the same bid with both and hope opener is a good guesser!

However, I have the answer to the dilemma and it is called Lebensohl.

Defence after Partner’s 1NT is Overcalled at the Two Level

The basic idea is that a 2NT invitational bid is replaced by a conventional 2NT, which is a ‘puppet’ to 3C. Responder can have a variety of hands including a long club suit and weak i.e. will pass opener’s forced 3C response.

1. Defence to a Natural Overcall

    1. Suit bids at the two level are to play.
    2. Double shows the values for a raise to 2NT (11-12 pts) and is basically for take-out (not
        necessarily with any values in the overcall suit). Opener will pass the double with a good
        holding in the suit.
    Otherwise will bid minimum hands in minimum ways and maximum hands in maximum
     ways (these ways can be precisely defined if you wish).
    Where an overcall is passed back to opener he may reopen with a double holding shortage in
     in the suit bid and support for the other suits (so responder may pass in tempo with a 10 or11
     count and a good holding in the enemy suit – you will pick up some of the penalties that the
     method makes difficult to get.) [Alternately the double can be played for penalties].
3. There are now two ways of getting to the three level ‘fast’ by direct bidding or ‘slow’ via 2NT.

The FASS method  - Fast Action Shows Stopper – uses:
1. Natural bids made at the three level as game forcing with 5+ card suits (may or may not
    have a stopper in the opponent’s suit)
2. A direct 3NT (fast) is to play (2 guards or 1 guard and a long strong minor.)
3. A direct (fast) cue-bid is Staymanic and shows a stopper.
4. 2NT is a puppet to 3C over which responder continues with:
    1. Pass                                = to play
    2. 3 of a suit that could not be bid at the two level        = to play
    3. 3 of a suit that could have been bid at the two level     = invitational
    4. A cue-bid (slow) is Staymanic and denies a stopper    = game forcing
    5. 3NT    (slow) shows a partial guard (Jxx, Qxx)         = game forcing
        Opener should remove if having no help.
You could use the alternative FADS i.e. fast action denies stopper. This means (among other things) that you will jump to 3NT to show no stopper…. personally I prefer my jumps to 3NT to be natural!

2. Defence to a Conventional Overcall
    These will always anchor to at least one named suit. The basic principles described above will
still apply, however some things will be different or unusual:
1. Cue-bid at the two level is Staymanic and shows a stopper (fast)
2. Cue-bid via the puppet 2NT denies a guard and is Staymanic (slow).
3. Pass followed by a double by responder is for penalties. A new suit after an initial pass by
    responder is competitive.
4. Where the conventional overcall shows two or three suits the double is probably best used
    as seeking a penalty and asking opener to double any runout he has a fair holding in.

Let us look at some carefully chosen examples.
The auction begins:  1NT  -  2H  -   You?

(1)    KQxxx            (2)    KQxxx            (3)    xxx
         xx                            xx                            xx
        Axx                          AK                          AJ
        xxx                           Qxxx                       AQJ10xx

    Bid 2S                          Bid 3S                     Bid 3C
    To play                  Forcing to game        Forcing to game

(4)    xxx            (5)    KJxx            (6)    xx
        AJ                      xx                         KJ10xx
        xx                      QJ10x                   Ax
       AQJ10xx            Axx                      QJxx

    Bid 3NT            Bid Double            Pass
                          A raise to 2NT         Smoothly!

(7)     AQxx            (8)    Jxx            (9)    AJ9x
          x                            xx                     Kx
         KJxx                      AJ10xxx            Qxxx
         KJ10x                    xx                      K109

    Bid 2NT                     Bid 2NT            Bid 3H
    then 3H (slow cue)     then 3D to play    Staymanic with a guard

(10)    Kx

    Bid 2NT
    then 3NT (partial stop)