[Kungsgeten]

This is a pretty popular start of a Stenbergs/Jacoby 2NT scheme, at least in Sweden:

1M--2NT;
3♣ = Artificial minimum
3♦+ = Extras

In some systems (usually playing limited opening bids) 2NT is used by opener in some sequences to show a max hand with support for responder's suit. For instance:

1♦--1M; 2NT = Max, 4+M
1♥--2♦; 2NT = Max, 4+♦

There's also other situations where 2NT confirms a fit and the 2NT bidder has painted a pretty good picture of his/her hand. Take this version of Odwrotka in Polish Club for instance:

1♣--1M; 2♦--2NT;
(1♣ = Strong or 12--14 NT, 1M natural, 2♦ = GF with 3+M support, 2NT = 5+M and a minimum hand, confirming a reasonable trump suit)

In these situations you can use 3♣ as the Stenbergs/Jacoby bid, and in response to this 3♦+ can have the same (or at least similar) meaning as your regular Stenbergs/Jacoby structure. If 2NT haven't already put us in a GF, then 3♣ does. I call this "Delayed Stenbergs", but perhaps there's already a name for this convention?

Here's a complete example of our Stenbergs structure:

1M--2NT;
3♣ = Artificial minimum. Resonder can now ask with 3♦ to find out about SPL as below. If no SPL then opener will cue bid at 4-level.
3♦ = Extras, no SPL.
3♥ = Extras. Singleton club. "Low shortness"
3♠ = Extras. Singleton diamond. "Medium shortness"
3NT = Extras. Singleton in the other major. "High shortness"
4X = Void (4♥ is void in other major)

And here's an example of a delayed Stenbergs auction with the same structure:

1♠--2♦; 2NT--3♣;
3♦ = No SPL.
3♥ = Singleton club. "Low shortness"
3♠ = Singleton heart. "Medium shortness" (but only two suits left so effectively high shortness)
3NT = 6♠, good suit.
4♣♥ = Void.

[steve2005]

Structure like this better than standard Jacoby. The jump to 4M on min really kills hands with slam tries. Other uses for 2N with limited hands handle Bridge World hand of death which is hard in standard.

[Kungsgeten]

steve2005, on 2015-October-10, 15:48, said:

The jump to 4M on min really kills hands with slam tries.

I agree. 4M should show something specific. Actually I believe our Stenbergs structure focus too much on short suits, but we're so used to it and it works fairly well so we continue to use it. Otherwise I like Mats Nilsland's version of Stenbergs 2NT (here 2NT shows a limit raise or better, so it could be tweaked further if playing 2NT as GF):

1M--2NT;
3C = Extras (GF), could have shortness
3D = Minimum
3HS = Extras with clubs/diamonds as side suit.
...3NT = Cue bid of opener's minor
...4m = Real support, changes trump suit (at least temporarily)
3N = Extras with other major as side suit.
4X = Extras with two singletons (5611, 6511 or 7411)

1M--2NT; 3C---
3D = Asks shortness (1 step = No, 2-4 step = Singleton, 5+ steps = Void)
3M = Limited hand, no slam interest. Opener shows void or bids serious 3NT with slam interest.
3NT = Suggestion to play
New suit = I got a short suit of my own

1M--2NT; 3D---
3M = Suggestion to play
3NT = Suggestion to play
3oM = Asks SPL