Nice to see a thread on this. I am currently learning Precision with my partner and we came across a few 4-4-4-1 hands in the opener's hand(=no impossible negative). I agree with rebidding 1NT with these hands over a positive 1-level response, but what to do over a negative? 1NT is a natural 16-18 No Trump opening now and the singleton is really a problem(1NT over positive is not necessarily a balanced hand).