manipulate
  1. v. To influence a person using means that would be less effective if the person knew your intentions.
manipulation
  1. n. The process of influencing a person using means that would be less effective if the person knew your intentions.
My definition relies heavily on descriptions I've read in two books. In Influence without Authority, Allan R. Cohen and David L. Bradford say, "influence attempts are not manipulative if you can tell your potential ally your intentions with no loss of influence."

Edgar Schein, in Process Consultation, Volume 1, defines manipulation as “influencing others without making visible the motivation behind the influence attempts.”

Each of these quotes suggests a test for whether your influence attempts are manipulative. Cohen and Bradford’s quote suggests what I call The Private Test of Manipulation: Could I tell the other person my intentions?

Schein’s definition suggests the second, stronger test, which I call The Public Test of Manipulation: Have I told the other person my intentions?