We investigate the existence of magnetohydrostatic equilibria for topologically complex magnetic fields. The approach employed is to perform ideal numerical relaxation experiments... We use a newly-developed Lagrangian relaxation scheme that exactly preserves the magnetic field topology during the relaxation. Our configurations include both twisted and sheared fields, of which some fall into the category for which Parker (1972) predicted no force-free equilibrium. The first class of field considered contains no magnetic null points, and field lines connect between two perfectly conducting plates. In these cases we observe only resolved current layers of finite thickness. In further numerical experiments we confirm that magnetic null points are loci of singular currents. (read more)