In traditional direct marketing, the implicit assumption is that customers will only purchase the product if they are contacted. In real business environments, however, there are "voluntary buyers," who will still make the purchase in the absence of a contact. While no direct promotion is needed for voluntary buyers, the traditional response-driven paradigm tends to target such customers. This paper presents "influential marketing," targeting only those whose purchase decisions can be positively influenced, i.e. buyers who are non-voluntary. Our novel, practical solution to this problem gives promising results.