In this paper we consider the problem of determining optimal block designs in experimental situations in which v treatments are applied to experimental units arranged in b blocks of size k where bh/v is not an integer. Using a minimization result proven in JACBOTJX (1989), some new methods for establishing optimality are derived which can often be used to establish the existence of optimal nearly balanced block designs within the classes of designs considered as well as the exact optimality of some specific types of nearly balanced block designs within classes where no other optimality results known to applicable