[Kungsgeten]

Partner and I currently play Flannery and 1H-1S as natural (5+ spades). However partner has suggested we skip Flannery and play Kaplan Inversion instead (I personally think we could play both, but that's another discussion). So what structure should we play after 1H-1S (1S show 0-4 spades, forcing NT style, could be GF if balanced)? I've previously constructed a relay methods, but that was in a Flannery context where opener could not have 4 spades. Our 1H opening shows 5+ hearts and 11-16 hcp.

My latest idea is inspired by Gazzilli/Häxan/Riton:

1H--1S;
1NT = a) Any max (about 14+-16) with less than 4 spades b) Minimum (11-14) with 3+ diamonds
2C = 3+ clubs, minimum
2D = 4+ spades, 11-16
2H = 6+ hearts, minimum
2S = 6-5
2NT = Not sure, perhaps solid heart suit?
3m = Not sure, perhaps 6-5?
3H = Good 7 card suit

1H--1S; 1N---
2C = GF vs strong hand (so about 10+)
2D = Preference or weak with own diamond suit
2H = Preference
2S = 4 spades, 5+ clubs, weak
2NT = INV vs minimum
3C = Weak
3H = INV with 3 hearts

1H--1S; 1N--2C;
2D = 3+ diamonds, minimum
...2H = Non-forcing (good preference)
...2S = Artificial GF
......2N = Balanced
......3C+ = 4+ diamonds
...2NT = INV with 4 diamonds
...3C = INV, 6+ clubs
...3D = INV, 5+ diamonds
...3H = GF
2H = 6+ hearts, max
2S = 4+ clubs, max
2NT = 0-5-4-4, max
3C+ = 4+ diamonds, max

I've been thinking about including max hands with 4 spades into 1NT too, but then we will easily miss a 4-4 spade fit when responder is weak and takes preference.

[Free]

After an unlimited 1♥ opening we used to play kaplan inversion with gazzilli. With a limited opening you can just skip the gazzilli. There's nothing really special about this structure:
1♥-1♠-?
1NT = 4♠
2m = natural, may be 5332
2♥ = 6+♥

After 1♥-1♠-1NT responder bids as follows (using XYZ for example):
2♣ = puppet to 2♦, usually invite hands or weak with ♦
2♦ = GF relay
2♥ = to play, 2(3)♥
2♠ = to play, (3)4♠
2NT+ = various INV+ distributional hands

[jdonn]

I used to play Kaplan Inversion in Precision, although I gave it up because the auction 1♥ P 1♠ DBL was too awful. This is what I liked:

1♥ - 1♠ (0-4 spades) -
1N = 4+ clubs or 11-13 balanced, NF
2♣ = 4+ diamonds
2♦ = 4 spades, 5-6 hearts
2♥ = natural
2♠ = 6 hearts 4 any, max (nice 14-15). Relayed to 2NT then you showed your side suit with 3♥ = 4-6 majors and 3♠ = 5-6 majors
2N = 6 hearts 14-15 balanced with stoppers
3♣ = 5-5 max, NF
3♦ = 5-5 max, NF
3♥ = natural

1♥ - 1N (5+ spades) -
2♣ = 4+ clubs or 2533 exactly.
All others natural, with 2♠ generally 3 card support.

1♥ - 1N - 2m - 2♠ (artificial GF like 4th suit forcing. 3om over 2m is natural 5-5 GF) -
2N = natural (4th suit stopped, at best xx of spades)
3m = natural 5-5
3om = doubleton spade
3♥ = natural
3♠ = no stopper in 4th suit or extra length anywhere, generally 15(43) with unbid minor unstopped.
These are essentially natural but wit 3om and 3♠ switched, which was very important since showing a doubleton spade was quite common but too space consuming if using 3♠.

[awm]

I'm sort of confused by Josh Donn's method, because the transfer rebids seem to give opener another chance to call (when responder accepts the transfer). This is really useful in a system with wide-range openings (so opener can transfer to diamonds and then bid again to pattern out on a big hand, rather than having to jump to 3♦ and run out of space), but seems not very useful in a precision system. With what hand does opener bid again after 1♥-1♠-2♣-2♦? Even the 6/4 reds hand is bidding 2♠ it seems.

Anyway, here's my contender after 1♥-1♠:

1NT = 3+♦ or 6+♥
2♣ = 3+♣
2♦ = minimum with 5♥/4♠
2♥ = maximum with 5♥/4♠

1♥-1♠-1NT:
... 2♥ = preference opposite red suits
... 2♦ = preference opposite red suits (opener bids 2♥ with 6+♥ and not diamonds)
... 2♣ = at least invitational
......... 2♦ = 3+♦ min
......... 2♥ = 6+♥ min
......... 2♠, 2NT, 3♣, 3♦ = max 3+♦, patterning out
......... 3♥ = max 6+♥