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.