Mixed raises

A mixed raise is a supporting bid that shows length in partner's suit and constructive values. It's stronger than a preemptive raise and weaker than a limit raise. It promises:

4+-card support for partner's suit
6-9 points with some defensive strength.

Mixed raises can provide an accurate description in a few different types of auctions. If you play Bergen raises over partner's major-suit opening bid, your 3C response (a constructive single raise with 4 trumps) is a mixed raise. The most common usage, though, is this jump cuebid after an opponent opens and partner overcalls a suit:

LHO Partner RHO You
1D 1H Pass 3D

Your jump cuebid of LHO's suit shows the mixed raise. It says nothing about your holding in diamonds. The same meaning applies if your RHO had made a negative double or responded 1S or 2C. As long as you can jump to three of opener's suit, it's a mixed raise.

A mixed raise is sometimes called "semi-preemptive". It differs from a standard preemptive raise in the location of your high cards. In the auction above, if you had jumped to 3H, it's a preemptive raise that shows 4+ trumps, but with no ace or king outside your suit -- a hand such as ♠104 ♥KJ107 ♦64 ♣Q9543. The mixed raise (a jump to 3D) shows the same trump support and could even be the same number of high-card points, but it promises a trick or so outside your suit -- a hand such as ♠104 ♥J1076 ♦64 ♣KQ954.

Note that a jump cuebid is a mixed raise only when:

An opponent opens and partner overcalls a suit. If partner opens the bidding, your cuebid of an opponent's suit is a stronger raise (limit or better).
The jump cuebid is at the 3-level. In the auction above, a jump to 4D would be a splinter raise that shows shortness in that suit and full values for game in partner's suit.

Other ways to raise an overcall

Here's a summary of the ways you can compete and show support after partner overcalls a suit.

LHO Partner RHO You
1C 1H 1S ?

Single raise (2H) = 6-9 support points, 3+ trumps.
♠K4 ♥J75 ♦K864 ♣9764
Jump raise (3H) = Preemptive. 3-7 points, 4+ trumps, no ace or king outside trumps.
♠J64 ♥KQ105 ♦108432 ♣4
Jump raise to game (4H) = Usually 5+ trumps with distributional values and fewer than 9-10 points, but could be a stronger hand.
♠643 ♥KJ1054 ♦K10943 ♣Void
Cuebid of their suit (2C or 2S) = Limit raise or stronger. 10-11+ points, 3+ trumps.
♠K4 ♥K75 ♦AJ104 ♣9764
Recommended: Agree that the cheaper cuebid (2C) shows 3-card support and the higher cuebid (2S) promises 4+-card support.
Jump to three of opener's suit (3C) = Mixed raise. 6-9 points, 4+ trumps.
♠74 ♥Q764 ♦AJ102 ♣863
Jump to 3 of responder's suit (3S) or 4 of any other suit (4C or 4D) = Splinter raise. Singleton or void in the bid suit, 14+ support points, 4+ trumps.
♠4 ♥KQ75 ♦KJ84 ♣A1064