Is there any way to reconcile the adaptationist’s image of natural selection as an engine of optimality with the more complex image of its dynamics we get from population genetics? This has long been an important strand in the controversy surrounding adaptationism, yet debate has been hampered by a tendency to conflate various different ways of thinking about maximization. Here I distinguish four varieties of maximization principle. I then discuss the logical relations between these varieties, arguing that, although they may seem similar at face value, none entails any of the others. I then turn briefly to the status of each variety, arguing that, while each type of maximization principle faces serious problems, the problems are subtly different for each type. In the last section, I reflect on what is at stake in the debate.