Disclosed herein are optical projection systems and related methods for projecting imagery employing shifting image position in-time to mitigate speckle. Exemplary optical systems may include a projector having a light source, a relay lens and at least one projection lens for projecting images. The relay lens or the projection lens may have at least one lens element that may be translated in-time substantially orthogonal to the optical axis of the optical system. Alternatively, the projection lens in its entirety may be shifted in-time to reduce speckle. Further, in stereoscopic embodiments, two projection lenses may be employed, wherein at least one element in each projection lens is moveable to shift the image in-time to reduce speckle. Moreover, electronic compensation, such as electronic addressing or image warping, for the image shifting may be employed to shift the image in a direction opposite to the speckle-reducing shift in position.