Systematists expect their hypotheses to be asymptotically precise. As the number of phylogenetically informative characters for a set of taxa increases, the relationships implied should stabilize on some topology. If true, this increasing stability should clearly manifest itself if an index of congruence is plotted against the accumulating number of characters. Continuous Jackknife Function (CJF) analysis is a new graphical method that portrays the extent to which available data converge on a specified phylogenetic hypothesis, the reference tree. The method removes characters with increasing probability, analyzes the rarefied data matrices phylogenetically, and scores the clades shared between each of the resulting trees and the reference tree. As more characters are removed, the number of shared clades must decrease, but the rate of decrease will depend on how decisively the data support the reference tree. Curves for stable phylogenies are clearly asymptotic with nearly 100% congruence for a substantial part of the curve. Less stable phylogenies lose congruent nodes quickly as characters are excluded, resulting in a more linear or even a sigmoidal relationship. Curves can be interpreted as predictors of whether the addition of new data of the same type is likely to alter the hypothesis under test. Continuous Jackknife Function analysis makes statistical assumptions about the collection of character data. To the extent that CJF curves are sensitive to violations of unbiased character collection, they will be misleading as predictors. Convergence of data on a reference tree does not guarantee historical accuracy, but it does predict that the accumulation of further data under the sampling model will not lead to rapid changes in the hypothesis.