The theory of coherent control of photodissociation with partially coherent laser pulses is developed and applied to the pump-dump control scenario of a collinear model of DH2. The coherence characteristics of the pump pulse are shown to be crucial for maintaining control over the product yield, whereas the coherence properties of the dump pulse are only of secondary importance. Control is shown to survive for partially coherent laser pulses, but only for a range of incoherence which precludes control with typical nanosecond pulsed dye lasers.