Group-randomized study designs are useful when individually randomized designs are either not possible, or will not be able to estimate the parameters of interest. Blocked and/or stratified (for example, pair-matched) designs have been used, and their properties statistically evaluated by many researchers. Group-randomized trials often have small numbers of experimental units, and strong, geographically induced between-unit correlation, which increase the chance of obtaining a "bad" randomization outcome. This article describes a procedure--random selection from a list of acceptable allocations--to allocate treatment conditions in a way that ensures balance on relevant covariates. Numerous individual- and group-level covariates can be balanced using exact or caliper criteria. Simulation results indicate that this method has good frequency properties, but some care may be needed not to overly constrain the randomization. There is a trade-off between achieving good balance through a highly constrained design, and jeopardizing the appearance of impartiality of the investigator and potentially departing from the nominal Type I error.