An auction got me thinking.
Your partner opens 1♥ and you bid 2♣, game-forcing. Partner rebids 2♥, and you bid 2NT. Partner repeats 3♥.
At this point, the contract will either be a notrump strain or a heart strain, right? So, any call except 3NT would be a cuebid in support of hearts. So far, so good.
However, what is partner's strength? This seems like a sequence where partner's strength is fairly unlimited. He might have a bare minimum opening. Or, he might have a powerhouse that is not right for an immediate 3♥ jump. This seems like a really good sequence for using Serious 3NT, but you just cannot do that.
Or, can you?
Suppose that you make a 3♠ call a relay to 3NT. If Responder wants to play in 3NT (or would have bid 3NT in this auction as "to play"), he bids 3♠, expecting that Opener will bid 3NT. If that was his intended contract, that's where we end up. Note that this relay would not risk a lead-directing double, because the person making the double would be on lead.
Using that approach, 3NT by Responder would instead be a cue of spades.
What this gains is that Responder can now relay to 3NT and then cue a minor if he has mere "cooperative" values. 3NT, 4♣, or 4♦ directly would be serious cues (3NT as a serious spade cue). With mere cooperative values any no minor control, Responder relays and then bids 4♥.
What if Opener rejects the relay? If Opener would not have passed 3NT, then he bids whatever he would have bid instead of 3NT. However, he should probably stretch to make a cue in support of himself if he would have bid 4♥, in case all was well in the world.
This same idea might work whenever hearts is agreed or is the sole focus suit and where the person bidding 3♠ over a trump-setting or focus-setting 3♥ call will be the declarer if the contract will be 3NT.
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