A graphical theory of habitat selection is built in steps. The theory treats two species in an environment with two usable patch types in a matrix of unusable space. The first step assumes habitat selection is density independent and free of search costs. The second assumes density independence, and the third assumes neither. The first two steps produce results already known from earlier theories. The third, however, requires a new analytical device, the isoleg, which is a line in a two—dimensional—state space of the two species' densities. An isoleg is a set of points in such a density space, such that on one side of the set, individuals of a species optimize their foraging by being strict habitat selectors, whereas on the other side, they do so by using at least a bit of a poorer patch. The population dynamics of the competitors is analyzed using their isolegs. The isolegs allow us to deduce that the zero isoclines of the species are warped into nonlinear forms capable of producing competitive coexistence. It is shown that at the equilibrium point of this coexistence, there may be no overt competition remaining. The difficulties this presents to the field investigator are mentioned, and a modified definition of interspecific competition is suggested.