The tests for zero partial association in a multiple contingency table have gained new importance with the introduction of graphical models. It is shown how these may be performed as exact conditional tests, using as test criteria either the ordinary likelihood ratio, the standard x squared statistic, or any other appropriate statistics. A strategy is presented for model selection, based exclusively on exact tests for zero partial association, performed initially in the full table and subsequently in appropriate marginal tables. This strategy is applied to a survey on stress in Danish primary school teachers. It illustrates that the usual asymptotic p-values are completely unreliable for large sparse tables. The appendix contains a computer printout of the complete seven-dimensional table analyzed in the article, plus all two-dimensional marginal tables. (Author/GDC)