Many randomized experiments in the social sciences allocate subjects to treatment arms at the time the subjects enroll. Desirable features of the mechanism used to assign subjects to treatment arms are often (1) equal numbers of subjects in intervention and control arms, (2) balanced allocation for population subgroups and across covariates, (3) ease of use, and (4) inability for a site worker to predict the treatment arm for a subject before he or she has been assigned. In general, a trade-off must be made among these features: Many mechanisms that achieve high balance do so at the cost of high predictability. In this article, we review methods for randomized assignment of individuals that have been discussed in the literature, evaluating the performance of each with respect to the desirable design features. We propose a method for controlling the amount of predictability in a study while achieving high balance across subgroups and covariates. The method is applicable when a database containing the subgroup membership and covariates of each potential participant is available in advance. We use simple simulation and graphical methods to evaluate the balance and predictability of randomization mechanisms when planning the study and describe a computer program implemented in the R statistical software package that prospectively evaluates candidate randomization methods.