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.