The described runout from 1NT - DBL was played for several years with a weak NT with rarely a poor result. The Moscow Rescue is simple and gives both opener and responder chances to show five card and four card suits. With a good hand, responder can also opt to sit for the double. And even when the opponents can collect on a penalty double, they must make the correct decisions every call to do it.
Principles
Following a double of 1NT in either the direct or the balancing seat, the first priority is to show a five card suit. PASS denies a five card suit unless that would end the auction. In that case REDOUBLE denies a five card suit.
After both have denied a five card suit, up-the-line bidding of four card suits begins. A four-three fit is acceptable. Often opener or responder develops a good picture of the combined hands and is able to pinpoint a four-four fit.
The Two Basic Auctions
When the opponents DOUBLE in direct position, responder will bid a five card suit, PASS without a five card suit, or REDOUBLE if willing to play 1NT-XX. Opener then bids a five card suit or will REDOUBLE. Responder then bids his lowest ranking four card suit. Opener can pass with a four-two fit if non-vulnerable and if opponents do not double. Or opener may choose to bid a four card suit at the two level.
When the opponents DOUBLE in the balancing seat, opener will PASS or bid a five card minor. Opener must not REDOUBLE, since responder will use that bid to deny a five card suit. Responder bids a five card suit or will REDOUBLE to keep the auction alive. Opener then bids his lowest ranking four card suit. Responder may PASS or bid a four card suit at the two level.
Transfer Variation
After a direct double of 1NT, responder can transfer his five card suit to opener.
Using transfers, responder can also show some 4-4 distributions, in the DONT style, by bidding again after opener bids 2 in response to responder's REDOUBLE.
After opener's rebid of 2
Playing transfers permits inferences to be drawn in the auction which begins INT - (DBL) - pass - (pass) - RDBL - (pass) Now responder's rebid of 2 shows 3-3-4-3 distribution, since: (1) with clubs and diamonds responder would start with 2, and (2) with diamonds and a higher-ranking suit responder would have REDOUBLED and rebid 2. Likewise, in the above auction, responder's rebid of 2 shows 3-4-3-3 distribution.