Stavig and Acock's recent attempt to extend theKstatistic under the special condition whenNis small was found to contain a number of basic errors. This paper corrects these errors, and reidentifies the problem as centering around the number of possible cell configurations in a contingency table given fixed marginals, and not smallNas they declare. In addition, procedures are provided for determining exact one-sided probabilities forKwhen the number of possible cell configurations is small.