Embedded in multidimensional nodal transport computations is the solution of transverse-integrated one-dimensional transport equations. Since, in these embedded one-dimensional computations, fluxes on boundaries are double P1 (DP1), it is generally assumed that the one-dimensional solutions, in the small-mesh limit, approach DP1 solutions. It is shown that this is not necessarily true. Small-mesh limits of nodal equations are derived, and it is shown that these are substantially worse than the DP1 equations under certain circumstances. Alternative nodal equations (which do have a DP1 small-mesh limit) are proposed.