Field experiments that involve nested structures frequently assign treatment conditions to entire groups (such as schools). A key aspect of the design of such experiments includes knowledge of the clustering effects that are often expressed via intraclass correlation. This study provides methods for constructing a more powerful test for the treatment effect in three-level cluster randomized designs with two levels of nesting (at the second and third levels). When the intraclass correlation structure at the second and third level is assumed to be known, the proposed test provides higher estimates of power than those obtained from the typical test based on level-3 unit means, because it preserves the degrees of freedom associated with the number of level-2 and level-1 units. The advantage in power estimates is more pronounced when the number of level-3 units (e.g., schools) is small and the samples are homogeneous (e.g., low-achieving schools). (Contains 2 tables.)