In this article, we assume partner opened 1NT (15-17).
As responder, with a five-card (or longer) MAJOR, I recommend always transferring. See this article.
But, with a five-card (or longer) minor, it is a completely different ballgame.
With the major, transferring allows you to play on the two-level. But, with a minor, a transfer puts you on the three level. Why would you want to play in 3 instead of 1NT if you held, say:
 instead of 1NT if you held, say:
 Q6
 Q6  J76
 J76  765
 765  Q8765?
 Q8765?
Just because you can transfer to a minor, doesn't mean you should transfer to the minor.
What if you held:
 KJ
 KJ  542
 542  AQ875
 AQ875  Q54?
 Q54?
Why bother showing the diamonds? You want to be in 3NT, so bid 3NT.
Just because you can transfer to a minor, doesn't mean you should transfer to the minor.
Even with a six-card minor, why show it if you want to be in 3NT no matter what? Raise 1NT to 3NT with:
 J4
 J4  J3
 J3  K32
 K32  KQJ765.
 KQJ765.
Just because you can transfer to a minor, doesn't mean you should transfer to the minor.
Why is this different from the handling of a five-plus card major? Because minors pay only 20 points a trick. To bid game in a minor, you need to be on the five level! When partner opens 1NT, I'd guess that five-of-a-minor is the right contract less than 2% of the time. If there is a game, it is "always" in 3NT or a major.
Furthermore, with a bad hand and a major, you can let partner play it on the 2 level. With a bad hand and a minor, you'd have to reach the 3 level (not something you want to do with only a 5-card minor).
If you have a decent hand with a four-card major and a longer minor, you can start with Conventional response to notrump to ask about majors Stayman and then show the minor. For example, responder to 1NT has:
 Q832
 Q832  --
 --  J76
 J76  AQ8652.
 AQ8652.
He starts with 2 . If partner bids spades, life is easy (raise to game). If partner doesn't bid 2
. If partner bids spades, life is easy (raise to game). If partner doesn't bid 2 , then the minor can be shown--3
, then the minor can be shown--3 (assuming the partnership plays this as forcing). In this case, responder doesn't want to insist on 3NT. But, with flat hands (as in the earlier examples), responder should insist on notrump instead of looking for greener pastures.
 (assuming the partnership plays this as forcing). In this case, responder doesn't want to insist on 3NT. But, with flat hands (as in the earlier examples), responder should insist on notrump instead of looking for greener pastures.
When would responder actually start with a transfer to a minor? (As to which system and how, you can read this article).
 (or 3
 (or 3 ) would have a better chance than 1NT. As examples, I'd prefer to play in three-of-my-minor with either of these hands:
) would have a better chance than 1NT. As examples, I'd prefer to play in three-of-my-minor with either of these hands: 3
 3  654
 654  QJ10965
 QJ10965  543 or
 543 or  6
 6  765
 765  43
 43  J765432.
 J765432.
 
In fact, when you have a weak hand and a 6+ card minor, I recommend always playing in 3 of the minor instead of 1NT (in 1NT, your minor will often produce 0 tricks!).
 K2
 K2  AJ7
 AJ7  KJ9765
 KJ9765  K3 or
 K3 or  Q5
 Q5  KQ8
 KQ8  K2
 K2  AJ10765.
 AJ10765. 
Start with a transfer and next bid 3NT. How will partner know you have slam interest? Because if you didn't, you would have just raised 1NT to 3NT. That is why it would be a big mistake to start with a transfer with something like:
 54
 54  32
 32  65
 65  AKJ9765 --you are always going to play in 3NT, so just bid it!
 AKJ9765 --you are always going to play in 3NT, so just bid it!
 --
 --  J6
 J6  Q1076
 Q1076  AKJ7654
 AKJ7654
 or  K42
 K42  5
 5  AJ9654
 AJ9654  A93.
 A93.
If you have no interest in playing in the minor, then don't transfer! If you might end up with your minor as the trump suit, then show it. It is as simple as that. Just because you can transfer to a minor, doesn't mean you should transfer to the minor.
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