The Stayman Convention is perhaps the most widely known of all bridge conventions (beyond Blackwood that is).  Lucky Sam Stayman.  He wrote an article in Bridge world in 1945 describing a convention invented by George Rapee and it became known as Stayman ever after.  This  convention is one that meets the three key criteria.  Most players who use the Stayman Convention apply it automatically whenever their partners open 1NT and they hold a four-card major.  There is little recognition that, all else being equal, flat hands usually play better in notrump than they do in a major suit.

For example - partner opens 1NT and you hold:
ª   7 6 5
©  K 5 2
¨  A J 5
§  Q 8 7
You are strong enough to press for game.  Should you employ Stayman to try for a spade game if partner has four spades?  No - this is just about the worse hand I can imagine for Stayman.  This 4-3-3-3 distribution offers no opportunity to ruff a side suit.  Keep in mind that partner’s hand is balanced (he opened 1NT, thus has no void or singleton).  This hand can only draw trump by ceding tricks to the opponents.  The bottom line is: with a flat hand you should expect to take the same number of tricks in notrump as in spades.  A nine-trick game in notrump sure beats down one in a ten-trick spade contract.

Overheard at the end of a bridge session:  Said Luc Lucie to her friend Duc Dory: “I bid and made one club on that last board”.  To which DD responded: “Really, that’s nice.  How’d the bidding go?”