A new method is described and illustrated which solves the planar, two vehicle collision reconstruction problem. The method, called LESCOR (LEast Square Collision Reconstruction), determines the initial velocity components when given: (1) final velocity components, (2) vehicle physical data, (3) damage geometry, (4) collision geometry and (5) the impact coefficients (restitution and friction). A novel feature is that if the impact coefficients are unknown but some of the initial velocity data is known (such as zero initial yaw rates and vehicle headings), the method will find the remaining initial velocities and the unknown coefficients. Using a six equation impact model and the method of least squares, LESCOR calculates any combination of 6 or less unknown initial velocity components and impact coefficients.Five example collision reconstructions are presented based on RICSAC collisions and a field example. The method has provided results which range from good to excellent and is superior to trial and error methods used in the past.