We demonstrate a simple method by which time-dependent interactions can be exploited to improve self-assembly in colloidal systems. We apply this method to two systems: a model colloid with a short-ranged attractive potential, which undergoes crystallisation, and a schematic model of cluster growth. The method is based on initially strong bonds between particles, to accelerate nucleation, followed by a stage with weaker bonds, to promote the growth of high-quality assembled structures. We track the growth of clusters during assembly, which reveals insight into effects of multiple nucleation events and of competition between the growth of clusters with different properties.