We present a method for regularising nonlinear registration which produces deformations which are biologically more plausible than conventional techniques. Our method, the Symmetric Prior for Regularisation of Elastic Deformations (SPRED), not only enforces diffeomorphism, but additionally penalises linear, planar and volumetric changes. Application of SPRED to the high quality NIREP dataset produced results whose quality matches that of established registration methods. The resulting deformations show significantly more plausible Jacobian distributions, both in terms of spatial locality and intensity. Future work will look to extend SPRED to include variable spatial priors, allowing different brain regions freedom to deform by varying amounts.