Mesoscale eddies mix ocean properties along locally neutral directions, but these neutral tangent planes do not form a well-defined surface.  While well-defined surfaces cannot be exactly neutral, the non-neutral errors can be made to be small.  Here we describe two different methods for forming these approximately neutral surfaces, emphasising the computational efficiency of the methods.  One method uses a relaxation procedure that is local in character.  This method is suitable to be used in forward ocean models that have a layered coordinate (such as MOM6).