On pp. 55–58 of Philosophical Problems of Statistical Inference (Seidenfeld 1979), I argue that in light of unsatisfactory after-trial properties of “best” Neyman-Pearson confidence intervals, we can strengthen a traditional criticism of the orthodox N-P theory. The criticism is that, once particular data become available, we see that the pre-trial concern for tests of maximum power (and for their derivative confidence intervals of shortest expected length) may then misrepresent the conclusion of such a test (or interval estimate). Specifically, I offer a statistical example where there exists a Uniformly Most Powerful test (a UMP-test), a test of highest N-P credentials, which generates a system of “best” confidence intervals (the [CIλ] interval system) with exact confidence coefficients. But the [CIλ] intervals have the unsatisfactory feature that, for a recognizable set of outcomes, the interval estimates cover all parameter values consistent with the data, at strictly less than 100% confidence.