Back to thinking about Kaplanville.

If 2H is a Fantoni-Nunes type bid, covering 10-13 with 6Hs or 5Hs with shape (but not including 4Ss), then 1H-1S(like a forcing NT)--1NT can cover the rest of the 10-13s with 5Hs. With a 5-4-3-1 one can decide whether to open 1H and rebid 1NT, or open 2H - in particular with 3Ss, one should open 1H to find a 5-3 S fit., and if 1S then open 2H to try to block a S overcall, since 2S by opps over 2H requires more values than 1S over 1H.

So 1H-1S--?

1NT: 11-14 not too shapely, not 4Ss, not good 14, could be 5-4-3-1 with 3Ss
2C: 13/14+, with a four card or longer minor, if less than 17 exactly 4 in minor and 5Hs
2D: 6+Hs
2H: 5Hs, 4Ss, up to 15
2S: 5H, 4Ss, 15/16-18, or 6-5+ in majors up to 16
3m: 14-16, 5-5+

One convention growing in popularity is 1m-jump to two level response to show 5+Ss and 4+Hs. For example, after 1D, 2H shows 5+Ss, 4+Hs and not close to an invite, and 2S shows 5+Ss, 4+Hs and an invite or close to it. The convention works fine when it comes up, and has some nice secondary effects as well.

For example 1D-1S--2H does not need to be played as promising 4Hs, just reverse values and no other good bid, or 3S and 6+Ds and extras. This allows opener to comfortably rebid 3D over 1S with a hand with too much for a mere 2D bid, but not enough to reverse. It also allows 2H to be rebid when looking for a 5-3 S fit when holding the values for a 3D rebid but with 3Ss.

Over 1D-1S--2H, responder rebids:

2S: Any hand with 5+Ss and fewer than 4Hs.

2NT: Weak hand, not enough for game opposite a minimum reverse. The only forcing calls now are 3H asking for a C stopper, and 4 of a minor.

3C/D: Natural, forcing to 3NT or 4D.

3H: Original game force with 5+S and 4Hs.

3S: Original game force with 5+S and 5+Hs.

3NT: About an original game invite with 4S, stoppers in Cs and Hc.

4C: Great fit for Ds, singleton/void in Cs, slam invite.

4D: Great fit for Ds, slam invite.

-----------

It is possible to use 1D-1H--2S likewise, playing that 1D-1H--1S is forcing with 4S, and the 2S showing a reverse with no other good bid, or with 3Hs and 6+Ds and extras. Here 3C by responder over 2S should show any hand with 5+Hs, to help find 5-3 H fits, and 2NT over 2S is the weakness bid.

-----------

If you pull 18-19 balanced out of the 1D opening (you should using either 1C, 2C or 2D to handle this range depending on system), then one can play:

1D-1S--2NT: Reverse with no other good bid, fewer than 3S.
1D-1S--2H: Raise with 3S, may have extras or reverse strength.
1D-1H--2NT: Reverse with no other good bid, fewer than 3H.
1D-1H--2S: Raise with 3H, has extras and perhaps reverse strength.

Over 2NT, responder bids 3C if weak, not enough for game opposite a reverse.

For direct 1NT overcalls, here's a section from ETM Gold Premium:

http://www.bridgematters.com/1ntover.pdf

Eric Kokish wrote a nice article in his ACBL bulletin column about balancing NTs - essentially one makes these wide ranging and then employs a 2C majors and range check.

The ETM notrump structure is up at:

http://www.bridgematters.com/etmnt06.pdf

This project took about a year as a result of a number of revamps. For the longest while design was for either or both major suit transfers to handle game invite hands, freeing up 2C for signoff or game force work. This proved to be poor.

A switch to using 2C for almost all game invites, and thus having most other bids as signoffs or game forces worked great. This parallels 1XYZ (two-way new minor forcing) where 2C is either a D signoff or any invite, and 2D handles the game force. A closer version of 1XYZ is:

2C: D signoff or any invite
2D: signoff with both majors, 4 only in OM, or a game force
2H/S,3C: signoffs
etc.