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tokens: of the solver in regions with steep gradients, can be used to mitigate this problem at the expense of making the method more diffusive. There are many different possible limiters, each trading stability and diffusion in a different way (e.g. Toro 2009 ). High-order slope estimation would be particularly challenging in our galaxy formation simulations. We model stellar feedback by directly modifying gas properties in cells surrounding young star particles, often resulting in sharp discontinuities within the density, velocity, and energy fields. We have chosen the MinMod slope limiter (e.g. Toro 2009 ) which is the safest choice in terms of suppressing instabilities, but consequently also the most diffusive. We find that, if we adopt a less diffusive slope limiter, the solution becomes unphysical; with the current implementation of feedback, we are hence required to adopt the MinMod slope limiter in order to maintain stability. In contrast, galaxy simulations accounting for strong stellar feedback via source terms in the Riemann solver, e.g. using a non-thermal pressure (Agertz et al. 2013 ; Kretschmer, Agertz Teyssier 2020 ), have successfully been carried out using slope limiters such as MonCen (Agertz Kravtsov 2015 ). We leave a more systematic investigation of this topic for future work, and instead focus here on a completely new solution to the diffusion problem. If neither the solver nor the cell size can easily be changed, the final alternative is to ensure the rate of flow relative to the grid is small. However, haloes with a naturally small net velocity are exceptionally rare. For example, in the region used by the EDGE project, of all haloes move at velocities greater than at the time of early star formation, z = 16. As we will see, this is unavoidable in cosmological volumes, and already enough to cause substantive numerical errors. Further, adding a spatially uniform velocity offset to the initial conditions cannot usefully reduce even a single halo’s net speed: the cosmological expansion ‘redshifts’ the momentum of particles. Any uniform velocity offset that is not associated with a potential gradient therefore decays proportionally to 1 + z ; in contrast, the physical velocities grow (during matter domination in the linear regime) as (1 + z ) −1 . Therefore, uniform velocity offsets rapidly become insignificant compared to the growing physical velocities. Our solution is to use the genetic modification approach (Roth, Pontzen Peiris 2016 ; Rey Pontzen 2018 ; Stopyra et al. 2020 ) to post hoc modify the initial conditions such that the velocity of a chosen halo is minimized, while its environment, accretion history and other properties are minimally affected. In fact, we have already adopted this approach as a matter of course for published EDGE results (Rey et al. 2019 , 2020 ). In this paper, we examine the effects of disabling the modification in one of our galaxies in order to compare the AMR solution with and without rapid