The observed stellar mass function (SMF) is very different to the halo mass function predicted by Λ cold dark matter (ΛCDM), and it is widely accepted that this is due to energy feedback from supernovae and black holes. However, the strength and form of this feedback is not understood. In this paper, we use the phenomenological model galform to explore how galaxy formation depends on the strength and halo mass dependence of feedback. We focus on ‘expulsion’ models in which the wind mass loading, β, is proportional to , with n= 0, 1, 2 and contrast these models with the successful Bower et al. model (B8W7), for which . A crucial development is that our code explicitly accounts for the recapture of expelled gas as the system’s halo mass (and thus gravitational potential) increases. While models with high wind speed and mass loading result in a poor match to the observed SMF, a model with slower wind speed matches the flat portion of the SMF at M★∼ 109–1011 h−1 M⊙. When combined with active galactic nucleus feedback, the model provides a good description of the observed SMF above 109 h−1 M⊙. In order to explore the impact of different feedback schemes further, we examine how the expulsion models compare with a further range of observational data, contrasting the results with the B8W7 model. In the expulsion models, the brightest galaxies are assembled more recently, and the specific star formation rates of galaxies decrease strongly with decreasing stellar mass. The expulsion models tend to have a cosmic star formation density that is dominated by lower mass galaxies at z= 1–3, and dominated by high-mass galaxies at low redshift. These trends are in conflict with observational data, but the comparison highlights some deficiencies of the B8W7 model also. The experiments in this paper not only give us important physical insight into the impact of the feedback process on the formation histories of galaxies, but the strong mass dependence of feedback adopted in B8W7 still appears to provide the most promising description of the observed Universe.