Transfer Walsh
A useful tool to find 5-3 and 4-4 fits in 
and 
after a preparatory 1
-opening is Transfer Walsh. Using this system, the 1-over-1 responses are switched around:
1 - ?
- 1
: 4+ (can have longer minor)
- 1: 4+ (can have longer minor)
- 1: 5+ (no 4/ unless strong)
Simply said, opener completes the transfer with exactly 3-card support, supports with 4-card support, and bids as if there was no transfer otherwise.
Accepting the major-suit transfer
This is almost forcing and shows exactly 3 cards in the transfer suit. Basically, the bidding has gone 1 - 1M - 1M. Game forcing hands can conceal the 3-card support.
Further bidding after 1 - 1
After responder virtually denies a 4-card major, opener has no need to bid one. The responses are:
1NT: 11 - 15 (semi-)balanced, may include hands like 4=3=1=5.
2: 11 - 15, 6+
2: 11 - 15, 3+
2/: Natural Reverse
Alternative method for sorting out the minors*
With this method you will place the 1NT contract in partner's hand, which is desirable.
1 - 1:
6 - 12 balanced
10+ with , can have 4-card major if GF
Opener responds as if partner has bid 1 - 1NT natural. After the signoff bid 1NT:
1 - 1 - 1NT - ?
2: 10+, both minors
2: 10+, long , no 4-card major
2/: GF, 4-card suit with .
2NT: Natural invitation
1 - 1NT: 5 - 9 with 5+
This method can be combined with NOT using inverted minors and 2 as GF raise in .
* Method by Micha Keijzers