This is my favourite technique.
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It reverses the sequence of requests used with the foot-in-the-door technique. Make a very large request that is likely to be turned down in order to increase the chances that people will agree to a smaller request later (the one desired in the first place).
For example, you wanted to apply for 2 weeks no-pay leaves during a very busy month. Approach your manager and asked to apply for 1 month. After rejecting your request, cut it down to 3 weeks and finally to 2 weeks. After rejecting you twice, chances are she may approve your 2 weeks no-pay leaves.
Another example, a conman after telling you his plights may ask for $50. After you have rejected him, he may continue to beg you until you give in to a much smaller amount maybe $2 - $5.
Any other examples?