My strategy is to ask a person for a letter, but then disqualify him or her if I detect any negative signs. For example, I might knock on one professor's door, enter the office and look for some sign of recognition on his face. If I don't see any, I might try to remind him that I took his class a year ago, that I often sat in the back and read The Aggie, that I sometimes ate my apple slices during lecture but always tried hard not to chew too loudly and disrupt class. If he still can't remember, I consider it a negative sign and disqualify him as a recommender. I look for other indications that a letter would be detrimental to my chances.
Laughter is a bad sign.
Looks of shock and horror are bad. A suggestion that I not pin all my plans upon acceptance, but rather, investigate the opportunities available in the growing food service industry, is bad. Eventually, I scrounge up enough people to fill the requirement. Then I realize I haven't beat Satan at all.