Optical tracking systems encounter a number of challenges, including turbulence and speckle. Atmospheric turbulence causes phase perturbations that distort the track imagery. Additionally, natural illumination of the object is sometimes insufficient, and the tracking system must illuminate the object with a laser. Laser illumination produces optical speckle, which is the breakup of the imagery into bright and dark patches. Speckle can be a severe source of noise for tracking systems. While existing theory predicts the impact of full-strength speckle on tracking performance for simple tracking algorithms (e.g., centroid) and simple objects (i.e., a circle or a square), the benefits of speckle mitigation remain unexplored for most practical cases. This work investigates the benefits of speckle mitigation for tracking. In particular, it considers polychromatic speckle mitigation, which spoils the temporal coherence (i.e., the coherence length) of the laser light to produce a narrow band of wavelengths, thus reducing the strength of the speckle. Using a physics-based software model known as PITBUL, tracking performance over a range of coherence lengths from 1 to 1,000 mm is investigated. The tracked objects are UAVs, and they follow a straight and level path for the first part of the simulation and execute a turn during the last few seconds. The simulation begins by creating a series of pristine images. Then, it degrades the images by adding the effects of atmospheric turbulence, transmission, backscatter, speckle, and sensor imperfections. Next, it tracks the object in the images using either the Fitts correlation algorithm or the centroid algorithm. Tracking performance is analyzed over several seconds by comparing the tracker's estimate of the track-point position to the actual track-point position. The results show that polychromatic speckle mitigation significantly reduces both the track jitter and the track drift.