We propose a method to generate ‘genetically modified’ (GM) initial conditions for high-resolution simulations of galaxy formation in a cosmological context. Building on the Hoffman–Ribak algorithm, we start from a reference simulation with fully random initial conditions, then make controlled changes to specific properties of a single halo (such as its mass and merger history). The algorithm demonstrably makes minimal changes to other properties of the halo and its environment, allowing us to isolate the impact of a given modification. As a significant improvement over previous work, we are able to calculate the abundance of the resulting objects relative to the reference simulation. Our approach can be applied to a wide range of cosmic structures and epochs; here we study two problems as a proof of concept. First, we investigate the change in density profile and concentration as the collapse times of three individual haloes are varied at fixed final mass, showing good agreement with previous statistical studies using large simulation suites. Secondly, we modify the z = 0 mass of haloes to show that our theoretical abundance calculations correctly recover the halo mass function. The results demonstrate that the technique is robust, opening the way to controlled experiments in galaxy formation using hydrodynamic zoom simulations.