An improved version of the random spatial phase modulator (RSPM) reported recently by one of us is described. Using the improved RSPM, a theoretical value of the SNR of several thousand can be achieved. Experimental results are presented verifying that speckle can be completely eliminated using RSPM. The measured SNR exceeds 100, and there is no visually detectable difference between images obtained with RSPM laser light and those with white light even for an optical system of f/600. The effective decorrelation distances for different diffusers and their dependence on the aperture of the RSPM are investigated. An application of RSPM to coherent spatial filtering is demonstrated.