A technique is presented to produce any desired partially coherent Schell-model source using a single phase-only liquid-crystal spatial light modulator (SLM). Existing methods use SLMs in combination with amplitude filters to manipulate the phase and amplitude of an initially coherent source. The technique presented here controls both the phase and amplitude using a single SLM, thereby making the amplitude filters unnecessary. This simplifies the optical setup and significantly increases the utility and flexibility of the resulting system. The analytical development of the technique is presented and discussed. To validate the proposed approach, experimental results of three partially coherent Schell-model sources are presented and analyzed. A brief discussion of possible applications is provided in closing