Penalty RedoubleExample: 1-D-R
After a takeout double of 1, if opener's partner has a balanced hand with 3-4 cards in Spades, Hearts, and Diamonds, and 10+ HCPs, he wants opener to cooperate in doubling whatever contract the opponent's end up in unless he opened a weak, distributional hand.
(But some people redouble with any 10+ HCPs.)
The redouble normally denies 4-card support for Clubs and also denies a 5-card major. (Bidding Dictionary)
Rebids By Opener
In Feb.2004 ACBL Bulletin, page 40, Eddie Kantar says that opener is supposed to pass with a full opening hand after responder redoubles, to give responder a chance to describe his hand.
Kantar says for opener to bid to show a weak, distributional hand, A very distributional hand may call for a jump rebid in the same suit (hand a little too strong to preempt the first time) or in a new suit with an extreme two-suiter.
4th Seat Redouble (e.g.: 1C-2S-D-R)In a sequence such as this, BidBase's default is 2+ card support with a top honor (Ace or King), allowing partner to underlead his top honor if he wishes.