This paper presents a fast, economical particle-multiple-mesh N-body code optimized for large-N modelling of collisionless dynamical processes, such as black-hole wandering or bar-halo interactions, occurring within isolated galaxies. The code has been specially designed to conserve linear momentum. Despite this, it also has variable softening and an efficient block-timestep scheme: the force between any pair of particles is calculated using the finest mesh that encloses them both (respecting Newtons third law) and is updated only on the longest timestep of the two (which conserves momentum). For realistic galaxy models with N > 10^6, it is faster than the fastest comparable momentum-conserving tree code by a factor ranging from ~2 (using single timesteps) to ~10 (multiple timesteps in a concentrated galaxy).
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