Historically, inbred progeny selection has been promoted as an effective means of improving both inbred and outbred performance, and in some cases as being superior to other methods. Advances in theory and new estimates of genotypic covariance components have allowed us to make better predictions of gain from inbred progeny selection than previously available. We developed predicted gain equations using a full model, based on new theory and estimates, and a reduced model, which contained only the additive genetic variance in the numerator, for three maize (Zea mays L.) populations, BS13(S)C0, BSCB1(R)C13, and 3L Comp (HS-S1)S1Outbred progeny selection was superior to inbred progeny selection for plant height and grain yield when the response unit was the outbred population. Inbred progeny selection was superior for plant height in both populations and more effective for grain yield in BS13(S)C0 in inbred response units. Negative estimates of the covariance parameter D 1 reduced predicted gain for inbred progeny selection in the full model in comparison to the reduced model when D1 was ignored.