I’ve mentioned before in passing that I like the idea of a variable 1NT opening bid, such as you often find in Acol systems. I think some of that attraction comes from seeing convenient minor bids get raised beyond the “follow up” 1NT rebid that would fully describe the hand. In Standard American, a minor suit bid at the one level followed by 1NT rebid shows a balanced hand with 12-14 points. This makes sense, and helps create the continuum of no trump point descriptions:

What you bid:	1 or 1 followed by 1NT	1NT	1 or 1 followed by 2NT	2NT	3NT
Points in hand:	12-14	15-17	18-19	20-21	Game

This is all very neat and tidy, and there are good reasons to have 1NT mean one very specific thing all the time. However, for a partnership that has agreed to use a weak 1NT when non-vulnerable, you can skip all of this “bid a minor and then bid 1NT” nonsense and simply bid a weak 1NT (so long as you’re not vulnerable, of course). By taking the one level completely out of the picture, you might prevent opponents from finding a comfortable entry into the auction. And partner knows to be very careful about raising you into the stratosphere.

There are, of course, other considerations: how do you handle five-card club or diamond suits in 5-3-3-2 distributions? If you play transfers of any type, do they apply to weak 1NT bids? What about Stayman? I’m sure there are others that I haven’t even begun to think about (like what happens if you overcall opponent’s bid with 1NT when you’re not vulnerable). But you might want to think about a system that leverages the flexibility of a variable 1NT.