The problem isn't what to do after 3♥, I think, it's what to do after 2♦. I know the Italians are playing an amped-up Gazzilli lately, I have some notes but they're all in Italian and I am too busy writing about pros & sponsors to labor over the translation just yet. It's on my list of things to do... In George's partnership with Alfredo and mine with Shannon, bidding 2 of the other major after 2♦ announces the strong hand and shows three pieces; responder asks with 2NT if she is interested in knowing more about your hand or places the contract if she couldn't care less. So your auction would go like this, playing "standard Gazzilli" -- 1♥ - 1NT; 2♣ - 2♦; 2♠ - 2NT; 3♦ - 3♥ ... 2♣, of course, showing either a minimum opener with 5+♥ and 4+♣ or any strong hand with 5+♥, 16+ high card points. We play 2♦ showing any 8+, nothing about anything else. In the auction above, you describe exactly twelve of your cards for partner -- 5 hearts, 3 spades, 4 or more diamonds. Judi and Shannon and Jenny and I play a slightly different treatment; when we have your exact opening -- 1♥ - 1NT, we know for sure partner doesn't hold 5 spades, so we use 2♠ to show the strong hand with six BAD hearts (and a jump to 3♥ over 2♦ to show six good ones). The reason to bid 2 of the other major to show the good hand is so that we never have to miss a 5-3 major suit fit. We won a whole basketful of MP in Boston when Judi and I got to play 4♥ on a Gazzilli auction that started 1♠ - 1NT, where opener had 16 or 17 high card points and responder had 10 with a 5 card heart suit. Standard bidders had to pass 2H in the auction 1♠ - 1NT - 2♥. It's helpful to spend some time discussing your partnership's style when mucking about in the majors -- does partner deny 4 spades when responding 1NT? Do you go through 1NT to show a 3-trump limit raise (makes life very hard in Gazzilliland if you do). What about holding 5 spades and 3 hearts when partner opens 1H? If I had to guess I'd say Judi and I have spent around 200 hours in partnership bidding working through these specific situations. I'm updating our Gazzilli notes this week and will publish them to the system notes section on my website (you'll find it under major suit openers). The section's very wordy, but you're welcome to stop by and browse. (With 5-7 flat, Nige, responder bids anything other than 2♦); 2NT denies two-card trump support, five of the other major and any six card minor. In the hand you gave I think you have an easy 4♥ bid. After partner's 3♥ call, it's just bridge. Judi bids 3♠, patterning out. And as much as I love to cuebid here, I wouldn't bid 4♣ unless I've specifically agreed with partner that 3♥ shows a limit raise with 3 trump (and I recommend that if you play limit raises like that you forget about 2♦ and jump to 3♥ over 2♣, just like the standard bidders.) :) As ever, ymmv.
