Zirconia: Better bidding after 1H-1S
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One of the more problematic auctions in (uncontested) standard bidding starts 1-1-2. The problem is that the fourth suit is available only at the three-level, leaving responder with no cheap way to create a strong auction. This simple convention solves this problem (and some others) at a very small cost. I'm sure others have developed similar methods but I haven't seen a good presentation anywhere.

Zirconia is a cheap fake way to show diamonds. After 1-1 opener's rebids are:

1NT: either 4+ or 2=5=3=3 in that order

All others are unchanged, except for the added negative inference that opener does not have three-card spade support.

Continuations are pretty standard, with 1-1-1NT-2 available as a cheap fourth suit bid. I prefer to use 4th suit invitational in this auction; this allows me to invite and get out in two of a suit. Playing this style, 1-1-1NT-2NT+ are natural and forcing to game.

This solves all the following problems:

1. Gives an easy force (and invite) when opener has the reds and responder has spades.

2. Solves a number of difficult hands where opener has three-card support,

3. Immediately disambiguates three- and four-card spade support.

The only real negative is the loss of the natural 1-1-1NT sequence. However, when opener has 3, the better of the major fits is often superior to 1NT. The problem is really only the 2=5=3=3 hand opposite a less-than-invitational responder with a singleton heart.

Zirconia with Gazzilli:

Gazzilli is a method where opener's 2 rebid is forcing one round, showing either clubs or a strong hand. This method greatly improves bidding on opener's strong hands and also frees up jumps to show distributional hands (like an intermediate 5/5). The main negative of Gazzilli is that you can no longer play in 2 in auctions like 1-1-2.

Gazzilli can be combined with Zirconia by making 1NT the two way bid after 1-1:

1NT: 4+, or 2=5=3=3, or any 17+ hcp hand

2: natural and not forcing

Others are unchanged from Gazzilli (so 3m can be 5/5, etc)

After 1-1-1NT:

2: 8+ points; opener can rebid 2 (NF) on a min with 3+

2,2,2: weak, to play opposite the reds

2N+: natural and game force