Cosmological simulations predict that dark matter halos with circular velocities lower than 30 km/s should have lost most of their neutral gas by heating of the ultra-violet background. This is in stark contrast with gas-rich galaxies such as e.g. Leo T, Leo P and Pisces A, which all have circular velocities of ~15 km/s (Ryan-Weber et al. 2008, Bernstein-Cooper et al. 2014, Tollerud et al. 2015). We show that when we include feedback from the first stars into our models, simulated dwarfs have very different properties at redshift 0 than when this form of feedback is not included. Including this Population-III feedback leads to galaxies that lie on the baryonic Tully-Fisher relation over the entire mass range of star forming dwarf galaxies, as well as reproducing a broad range of other observational properties.