The integration of the simplest of the equations governing a compressible hydromagnetic equilibrium (Woltjer 1960) with a density distribution similar to that of actual stars results in a magnetic field whose strength is roughly proportional to the density throughout most of the star. Hence there may exist strong central magnetic fields whose only observable effect is a distortion of the star as a whole. Surfaces of constant density in distorted magnetic stars are expected to be spheroidal. A variational calculation results in a simple formula for the eccentricity of the spheroids, provided that it is small. On the basis of particular models for the density, it is concluded that the distortions are significant if the magnetic energy is 6 per cent or more of the gravitational potential energy. For the models considered, the spheroids are found to be prolate.