© 2016 The Authors. We describe a NOVel form of Adaptive softening (NOVA) for collisionless N-body simulations, implemented in the RAMSES adaptive mesh refinement code. In RAMSES - that we refer to as a 'standard N-body method' - cells are only split if they containmore than eight particles (amass refinement criterion). Here, we introduce an additional criterion that the particle distribution within each cell be sufficiently isotropic, as measured by the ratio of the maximum to minimum eigenvalues of its moment of inertia tensor: n = λmax/λmin. In this way, collapse is only refined if it occurs along all three axes, ensuring that the softening ε is always of order twice the largest interparticle spacing in a cell. This more conservative force softening criterion is designed to minimize spurious two-body effects, while maintaining high force resolution in collapsed regions of the flow. We test NOVA using an antisymmetric perturbed plane wave collapse ('Valinia' test) before applying it to warm dark matter (WDM) simulations. For the Valinia test, we show that - unlike the standard N-body method - NOVA produces no numerical fragmentation while still being able to correctly capture fine caustics and shells around the collapsing regions. For theWDM simulations, we find that NOVA converges significantly more rapidly than standard N-body, producing little or no spurious haloes on small scales. We will use NOVA in forthcoming papers to study the issue of halo formation below the free-streaming mass Mfs; filament stability; and to obtain new constraints on the temperature of dark matter.