Now it seems to all us that the Jarque-Bera test when applied to short samples is improper and leading to a wrong results: we intend though a sample could eventually be drawn from a normal Distribution, not else. I think we should check the two parameters Skewness, S, and Excess Kurtosis, k, separately. The difficulty arises how to perform the test: how to chose the individual confidence in order to be sufficiently assured that the sample follows, or not, the normality hypothesis. Note that, except to exceptional cases perhaps, we naturally chose to set the same confidence level for each test: a Confidence Interval for regarding S, other k. Two ways are immediately open: a) both inside the C.I. say 5% significance, b) include/capture as well the outputs consisting in one, whatever, parameter be *capture*, and using a compensatory factor penalizing the latter occurrence against the one consisting in double capture.