The self—thinning rule predicts that for a crowded even—aged plant population a log—log plot of average plant mass vs. plant density will reveal a straight "self—thinning" line of slope–3/2. The rule is supported by examples from many individual populations, and by the existence of an interspecific relationship that yields a line of slope–3/2in a log—log plot displaying average mass and density data from many populations of different species. I examined and reanalyzed the evidence to evaluate the strength of support for this widely accepted rule. Some problems in fitting thinning lines and testing agreement with the rule have no truly satisfactory solution, but three improvements on commonly used methods were made: the analysis related stand biomass density to plant density because the alternative of relating average plant mass to plant density is statistically invalid; principal components analysis was used rather than regression, because regression relies on unrealistic assumptions about errors in the data; and statistical tests of hypotheses were used to interpret the results. The results of this reanalysis were that 19 of 63 individual—population data sets previously cited in support of the thinning rule actually showed no significant correlation between stand biomass density and plant density, and 20 gave thinning slopes significantly different (P<.05) from the thinning rule prediction. Four other analyses provided additional evidence against a single quantitative thinning rule for all plants: slopes of the thinning lines were more variable than currently accepted, differed significantly among plant groups, were significantly correlated with shade tolerance in forest trees, and differed among stands of the same species. The same results held for the intercepts of self—thinning lines. Despite the failure of the thinning rule for individual populations, the combined data for all populations are still consistent with an interspecific relationship of slope–3/2; therefore, the existence of the interspecific relationship does not necessarily support the within—population thinning rule. The within—population and interspecific relationships are apparently different phenomena that may arise from different constraints, so the two relationships should be tested and explained separately..