Tapping on surfaces in a typical virtual environment feels like contact with soft foam rather than a hard object. The realism of such interactions can be dramatically improved by superimposing event-based, high-frequency transient forces over traditional position-based feedback. When scaled by impact velocity, hand-tuned pulses and decaying sinusoids produce haptic cues that resemble those experienced during real impacts. Our new method for generating appropriate transients inverts a dynamic model of the haptic device to determine the motor forces required to create prerecorded acceleration profiles at the user's fingertips. After development, the event-based haptic paradigm and the method of acceleration matching were evaluated in a carefully controlled user study. Sixteen individuals blindly tapped on nine virtual and three real samples, rating the degree to which each felt like real wood. Event-based feedback achieved significantly higher realism ratings than the traditional rendering method. The display of transient signals made virtual objects feel similar to a real sample of wood on a foam substrate, while position feedback alone received ratings similar to those of foam. This work provides an important new avenue for increasing the realism of contact in haptic interactions.