A multiple comparison technique for simultaneous inference in the nonstandard randomized block design models considered by Graybill [3] and Scheffé [11] is developed. Its computation and properties are discussed in terms of a clinical trial. The technique involving a number of independent tests with possibly unequal sizes, not the well-known Bonferroni tests [5], is appropriate when most contrasts between the treatments are of interest, but a few of the comparisons are of primary importance.