We propose a method based on quantitative theoretical analysis for achieving speckle contrast of 1% or less in images created by a full-frame laser projection display system. The method employs a stationary multimode optical fiber to achieve the effect of using a rapidly moving diffuser, but without moving the fiber or any other system component. When a suitably large projector lens is used, low-speckle illumination light delivered through the fiber acts in conjunction with wavelength diversity at the projection screen to achieve speckle contrast of 1% in viewed images. We describe in detail how the proposed method might be used with most types of high-power visible lasers being considered for large-venue displays. When used with visible laser diodes, the method may also be suitable for use in laser-based television.