We investigate the choice of compensation scheme by firms. Our basic model shows that the unique equilibrium choice for profit maximizing duopsonists in a labor market is for one firm to offer a wage rate and for the other to offer a piece rate. This result arises because the firms recognize that, by offering different compensation schemes, they induce self-selection among workers, which thereby decreases the intensity of competition in the labor market. We find this asymmetry to be robust to allowing for firing, free entry, and a class of more general compensation schemes. When we broaden our model to permit firms to be differentiated in the eyes of workers (either geographically or by “other working conditions,” e.g.), we find that our results are preserved when differentiation is low, but that both firms choose to offer a piece rate when differentiation is high.