Velocity filtering is a means of detecting weak point targets in imagery sequences. Pixel intensity is accumulated under an assumed target velocity and detection is predicated upon this cumulative intensity. However the unknown target velocity necessitates implementation of an entire bank of velocity filters, which requires dedicated hardware in order to be feasible. This paper describes some heuristic search methods which may be used to facilitate implementation of velocity filtering on a sequential computer. Criteria for ordering a pixel-first search through the candidate space are described. A best-first paradigm is also suggested as an alternative to pixel-first search. Monte-Carlo simulations show that both approaches are more efficient and yield better results than an arbitrary-order search of the candidate space.