If an observable x does no or only barely overcome the error inherent
in an experiment designed to measure x then the extraction of informat
ion, e.g., of an upper limit on x, is plagued with conceptual difficul
ties. They are discussed in the present note. It is concluded that the
bayesian concept offers a satisfactory answer. It is applied to the r
eanalysis of tests on time-reversal symmetry breaking via detailed bal
ance.