Summary: A “curvature correction”, in the sense used herein, is model fragment that is intended to account for some proportion of the error that is introduced into explicit algebraic Reynolds-stress models as a consequence of ignoring the convective transport of stress anisotropy within a framework in which the velocity vector and stress tensor are represented in terms of Cartesian components in highly-curved flow conditions. The present paper examines the ability of such corrections to represent this error, based on a-priori investigations of representative 2-D and 3-D massively separated flows for which the ‘exact’ level of the stress transport is known. In essence, the corrections reflect the assumption that the convection of the Reynolds-stress components, or the associated strain-tensor components, expressed in terms of curvature-oriented coordinates, is negligible. The analysis shows, first, that in general recirculating flows, the contribution of anisotropy transport to the stress balance is generally small, so that any form of related correction is of little consequence. Second, the variants of curvature correction examined correlate poorly with the real anisotropy convection. Thus, while these curvature corrections are useful in very particular conditions, such as flow in highly-curved ducts, they are not generality effective - indeed, possibly counterproductive - and cannot be recommended for inclusion in general numerical schemes.