A fluid dispenser includes a dispense mechanism that provides for increased mechanical advantage. The dispense mechanism includes a lever member and an actuator. The lever member includes a first lever section that receives application of an input force and a second lever section that applies an output force to the actuator. The lever member and/or the actuator are configured to provide at least two contact points between the actuator and the second lever section during the course of a dispensing stroke such that the mechanical advantage provided at a first one of the at least two contact points is greater than the mechanical advantage provided at a second one of the at least two contact points.