One of the key problems in theoretical biology is the identification of the mechanisms underlying the evolution of complexity. This paper suggests that some difficulties in current models could be avoided by taking account of “niche selection” as proposed by Waddington  and subsequent authors . Computer simulations, in which an evolving population of artificial organisms “selects” the niche(s) that maximize their fitness, are compared with a Control Model in which “Niche Selection” is absent. In the simulations the Niche Selection Model consistently produced a greater number of “fit” organisms than the Control Model; although the Niche Selection Model tended, in general, to produce organisms occupying simple niches, it was nonetheless more effective than the Control Model in producing well-adapted organisms inhabiting complex niches. It is shown that the production of these organisms is critically dependent on the rate of environmental change: Slow change leads to fit but undifferentiated populations, dominated by organisms occupying simple niches; differentiated populations, including well-adapted organisms living in complex niches, require rates of environmental change lying just beyond a mathematically well-defined critical value. In simulation “Niche Selection,” unlike conventional “Natural Selection,” provides a permanent selective bias in favor of simplicity. This tendency is counterbalanced by statistical forces favoring shifts from rare “simple niches” to commoner niches of greater complexity. Fit organisms inhabiting complex niches only emerge in conditions where the rate of environmental change is high enough to avoid the concentration of the population in very simple niches, but slow enough to permit step-by-step adaptation to niches of gradually increasing complexity. This result appears to be robust to changes in simulation parameters and assumptions, and leads to interesting conjectures about the real world behavior of biological organisms (and other complex adaptive systems). It is suggested that some of these conjectures might be relatively easy to test.