Defending against a strong 1
An strong 1-opening just screams to be disturbed, and many a system has been devised to do just that. The one that I currently play is non-forcing Suction (which is similar to Suction).
Suction is a simple defence against a strong Club. A suit either shows the next suit or the two suits below the bid suit. For example shows either or +. 1NT shows a 2-suiter in two non-touching suits (either + or +. Double is treated as a -overcall. The problem with this defence is that the opponents have a double shot because your bid is (almost) forcing. The solution is very simple:
In this variant, a suit overcall shows the suit you bid or the next two suits, so for example a overcall shows either or + . The complete scheme looks like this:
1 - ?
- Dbl: or +
- 1: or +
- 1: or +
- 1: or +
- 1NT: + or +
- 2: or +
- 2: or +
Now you have taken away the double shot. Responses follow Chris Ryall's ParadoX style. I will give an example:
1(strong) - 2 ( or +) - pass - ?
pass: Not willing to play 3 opposite
2/: Preference opposite 2-suiter, support for .
2NT: Asking bid
3: Support for , willing to play a red suit at the 3-level opposite a 2-suiter.
A redouble by responder shows either equal length support or 1-card better support for the lower suit (and 3-card support for the 1-suiter). Overcaller will now bid the upper suit if it is longer and the lower suit in all other situations.
If you have the 2-suiter variation and you were doubled you can bid the lower suit if it is longer, else redouble for SOS.
The range problem
If 1 by opponents was forcing with unlimited strength (some Multi-way bid, or Precision-style), all the bids above are very agressive overcalls. If you do have a very good hand, you might have a range problem. The solution is simple: With hands too strong to overcall directly, pass first and bid later. As it is imperative to bid now if you want to disturb their auction, passing first and bidding later is illogical. Therefore, it must show a good hand. Experience learns that if you have a good hand, chances are good that either responder makes a negative response, or opener has a weak variant of his bid. In either case, bidding will not have gone very fast in the first round, and you have the opportunity to make your bid.
The danger of NF Suction
All players can pass after your Non-forcing Suction bid. If you have the 2-suiter, this means that partner did not have support for the suit you are playing in now. Odds are you are in a 3-2 fit or worse. Normally this is only a problem if the vulnerability is unfavorable. Another thing to note is that the opponents are not likely to pass out your overcall, even if they both have length. It just does not feel right to have the auction 1 (2) pass (pass) pass. But it can happen, and that's exciting!
The strong 2 or 2NT
You can play the same after a strong 2 or 2NT (or some other strong opening bid), just one level higher! This opening bid also screams for overcalls. Just be careful, because partner does not have much.