An ideal ordination method would have known properties with respect to an explicit, order invariant ecological response model defined in more than one dimension. The Curtis-McIntosh model (each species weakly unimodal) is a good general-purpose model of a single gradient, but not current method is guaranteed to dispose samples from such a gradient along a straight line. There is some theoretical justification for using reciprocal averaging (RA), or local non-metric multidimensional scaling (NMDS) with Kendall's simple similarity coefficient, but the former tends to produce arches rather than straight lines and the latter can produce erratic curves (as illustrated here by applying the method to simulated coenocline data). The non-metric method is nevertheless shown to perform well (a) with high beta-diversity plant distribution data and (b) with simulated coenoplane data, where its performance is better than that of RA. Results with coenoclines and coenoplanes concur with those of Fasham (1977) who tested NMDS with a different coefficient. Local scaling is shown to be preferable to global, and primary tie treatment to secondary, in tests on coenocline and coenoplane data. A possible alternative non-metric approach is mentioned.