By combining test-particle and self-consistent techniques, we have developed a method to rapidly explore the parameter space of galactic encounters. Our method, implemented in an interactive graphics program, can be used to find the parameters required to reproduce the observed morphology and kinematics of interacting disk galaxies. We test this system on an artificial data-set of 36 equal-mass merging encounters, and show that it is usually possible to reproduce the morphology and kinematics of these encounters and that a good match strongly constrains the encounter parameters. An update to this software with additional capabilities, Identikit 2 (ascl:1102.011), is available.