Using quantitative genetic theory we develop predictions for the evolution of trade-offs in response to directional and correlational selection. We predict that directional selection favoring an increase in one trait in a trade-off will result in change in the intercept but not the slope of the trade-off function, with the mean value of the selected trait increasing and that of the correlated trait decreasing. Natural selection will generally favor an increase in some combination of trait values, which can be represented as directional selection on an index value. Such selection induces both directional and correlational selection on the component traits. Theory predicts that selection on an index value will also change the intercept but not the slope of the trade-off function but because of correlational selection, the direction of change in component traits may be in the same or opposite directions. We test these predictions using artificial selection on the well-established trade-off between fecundity and flight capability in the cricket, Gryllus firmus and compare the empirical results with a priori predictions made using genetic parameters from a separate half-sib experiment. Our results support the predictions and illustrate the complexity of trade-off evolution when component traits are subject to both directional and correlational selection.