When defending a Michaels cue bid showing two known suits, it is common to use Cue Bids of the shown suits to show an invitational or better raise of opener's suit and an invitational or better values and length in the 4th suit. See Larry Cohen's "Versus Michaels or Unusual Notrump" article for a discussion.
When a Michaels Cue Bid shows a 2-suiter with 1 known suit, the situation is more difficult because only 1 cue bid is available, and responder may wish to compete in either minor, or force in a minor. After 1♠-(2♠) showing hearts and an unspecified minor, a response of 3♣ or 3♦ could be played as forcing. If 3m is forcing, responder must pass with a competitive hand, and the auction may reach an uncomfortable level. If 3m is played as competitive, what should responder do with a forcing hand. They could double to show values and willingness to penalize a suit, but that leaves the partnership poorly positioned if advancer supports the known suit.
In the July, 2006 isse of "The Bridge World", Jeff Goldsmith recommended playing transfers over a 2-suited overcall with 1 known suit. Playing transfers, responder can bid 2NT to show clubs, and 3♣ to show diamonds. If opener wouldn't take action over a competitive 3m response, opener completes the transfer. If opener would take action over a competitive 3m response, opener bids naturally.
Transfers provide 3 ways to raise opener's suit: a cue bid of the known suit, a transfer into opener's suit, and raisiing opener's suit. Your partnership can decide how to use the 3 raises. In their "Mixed Raises Part 1: How to Bid and Defend Against Them" article, Steve Weinstein and Dan Wolkowitz advise "a mixed raise conveys both trump length and strength to partner. This could be crucial when the opponents also have a fit. If the auction is at the 5-level by the time your partner makes his next call, at least you have conveyed the rough offensive and defensive potential of your hand." Because of the value of mixed raises in competitive auctions, my preference is to use a transfer to opener's suit to show a mixed raise, a cue bid to show an invitational or better raise, and a direct raise to show a competitive raise.
With that agreement, after 1♠-(2♠):
- 2NT = ♣
- 3♣ = ♦
- 3♦ = mixed raise
- 3♥ = invitational or better raise
- 3♠ = competitive raise
After 1♥-(2♥):
- 2♠ = invitational or better raise
- 2NT = ♣
- 3♣ = ♦
- 3♦ = mixed raise
- 3♥ = competitive raise
Those preferring to immediately differentiate between invitational and game forcing raises can drop the use of the transfer into opener's suit to show a mixed raise, and use the cue bid and the transfer to distinguish game forcing and invitational raises.
