Cappelletti (a.k.a. Hamilton) is a very popular defense against 1NT openings. Here's how it works:
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Note that you can still double a 1NT opening for penalty: this is the main advantage of Cappelletti over most other systems. The disadvanatge is that you often end up at the 3-level with a two-suited hand (sometimes with a 7-card fit).
Finding a Fit
After you overcall 2 (showing a one-suited hand), your partner should usually relay to 2. You can then pass (with diamonds) or bid 2, 2, or 3 to show your suit.
After you overcall 2 (showing both majors), your partner will usually sign off in 2 or 2. Similarly, your partner will usually sign off in 3 or 3 after your overcall 2NT.
After you overcall 2 or 2 (showing the specified major and an unspecified minor), your partner can pass if he has support for your major, or bid 2NT to ask for your minor.