Responsive Doubles (RDs) are played in a variety of ways after LHO has opened, and 2nd and 3rd seats have acted.
Bridge Conventions Complete (BCC) defines RDs as a double --
Modern Bridge Conventions, by Bill Root and Richard Pavlicek, and Overcalls, by Mike Lawrence, both say that if RHO bids a new suit rather than raising, a double is for penalty, not an RD. In fact, ML says that the raise by RHO is the most important point of the convention and explains why. (See his book.)
However, The Bidding Dictionary, by Alan Truscott, says that a double after 3 suits have been bid (or even 1x-1y-1N) shows 5 (rarely 6) of the unbid suit and usually a doubleton in overcaller's suit. We use this approach in BidBase, so if you want Double to be penalty when RHO bids a new suit, you will need to deactivate the RD entries and activate the Penalty Double entries.
Most sources agree that a double is not an RD if --
Doubling with 3-card major support:
Mike Lawrence says that with KQ7 KJ9 8754 974, after 1C-D-2C, you can double with only 3 cards in each major because of the excellent high cards.
But a couple of paragraphs later, he also doubles with Q97 KJ3 in the majors, where Q97 isn't all that great. This is a little bit of a contradiction, but he says that doubling. even with the weaker hand, is better than passing. Deselect it if you don't like it.
If the opponents have bid and raised a major, then if you had 4+ of the other major, you would normally bid it, so an RD in this situation normally shows the minors and denies 4 of the unbid major.
If partner bids the unbid major (hoping you have 3) when you only have 2, you will have to correct to Clubs.
This may be survivable after 1H-D-2H when you can correct 2S to 3C, but after 1S-D-2S, if doubler bids 3H, you have to correct to the 4 level. The key seems to be that in this case, partner should not bid 3H unless he made a TOX with 5+ Hearts; otherwise, he should bid his better minor.
What would you bid with 8654 K2 QJ8 JT85 after 1H-D-2H?
Lawrence says (Overcalls, page 114) to double because even though you only have 3 Diamonds, they are good. We haven't put this in BidBase because we are still mulling that over. At best, you are going to be on the 3 level with an anti-LOTT 5-3 fit.
Likewise, Lawrence says (also page 114) to double after 1-D-2 with 872 QT84 KJ7 T65 if you play that a correction to 3 (if doubler bids 3) shows a weaker hand than an immediate 3 bid. Again, you are at the 3 level with only an 8-card fit.
Upper Limit For Responsive Doubles
You (and your partner) must decide at what level a double is penalty rather than Responsive. Many people play that a double of a bid of 3S is Responsive, but of any higher bids, penalty.