Responder’s direct cuebid is a disputed and under-discussed topic. There are two popular usages of this bid:

• Limit raise or better
• Generic game force

I suggest different approaches to major and minor openings.

After a major opening

The cuebid is a limit raise or better. From the pigeonhole principle, you have either of these:

• 3-card support
• 5-card unbid suit
• 4-4 unbid suits
• 4-card adverse suit

The promise of a fit clears the way for finding a game. Other calls better describe game-forcing hands without 3-card support.

• 5-card unbid suit: free bid
• 4-4 unbid: negative double
• 4-card adverse suit: 3NT

After a minor opening

We make the cuebid a versatile tool to combine the advantages of popular treatments.

According to the previous section, you can have an embarrassing strong hand with no 4-card support, no biddable side suit, and no stopper in the adverse suit. Imagine holding the following hand at 1♣-(1♠)-?

♠ xxx
♥ Axx
♦ Axxx
♣ Axx

You could have bid 3NT if RHO did not overcall, but you cannot now because there is no spade stopper. You are wary of passing because 3NT is still playable if your partner has a spade stopper. Ask for one with 2♠.

Besides, we can keep the limit raise. Your partner is eager to show a stopper as notrump games score more than minor games. Including the limit raise in the cuebid does not affect the bidding structure.