Using the gradient-based approach to computing optical flow as a basis, this paper introduces the use of multiple constraints to aid in the solution of the optical velocity. The primary constraints are (1) the image luminance that corresponds to a given point in the world is constant from one frame to the next and (2) the motion is smooth from one point to the next. Multiple constraints are derived from the original luminance image through the application of standard spatial operators. These are then used in the same equation as the luminance constraint to derive a set of equations (one for each constraint), each with two unknowns (the spatial components of the optical velocity). This brief paper requires a good understanding of the problems and techniques of optical flow and only reports on an extension of the basic technique intended to simplify and improve the computational technique.