Digital holography enables the creation of multiple optical traps at arbitrary three-dimensional locations and spatial light modulators permit updating those holograms at video rates. However, the time required for computing the holograms makes interactive optical manipulation of several samples difficult to achieve. We introduce an algorithm for computing holographic optical tweezers that is both easy to implement and capable of speeds in excess of 10 Hz when running on a Pentium IV computer. A discussion of the pros and cons of the algorithm, a mathematical analysis of the efficiency of the resulting traps, as well as results of the three-dimensional manipulation of polystyrene micro spheres are included.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.