In this paper, implementation of the complex screen approach for generating partially-coherent Schell-model sources using phase-only control, like that available using commercial-off-the-shelf liquid-crystal spatial light modulators, is presented. Previous techniques for generating Schell-model sources have used phase-only spatial light modulators in combination with amplitude filters to produce partially-coherent fields. Using amplitude filters complicates the optical set-up and significantly reduces the flexibility of the system. Here, both analytically and with simulations, it is shown that both the amplitude and phase of the source field can be manipulated using phase-only control. This contribution removes the need to use amplitude filters, thereby simplifying the optical set-up and increasing the system's flexibility.