Resolvable block designs are used in statutory crop variety trials in the United Kingdom. An algorithm for constructing suitable designs for this purpose has been described by Patterson and Williams (1976a). When seed is in short supply or some other economy is enforced, the trials sometimes have to be conducted in only two replications. It is important in these circumstances to use the most efficient possible designs. Bose and Nair (1962) have described and tabulated a series of two-replicate resolvable designs. Another series of designs is given by the duals of the resolvable paired-comparison designs of Williams (1976). Both series involve the use of symmetric block designs. Patterson and Williams (1976b) have shown that every two-replicate resolvable design is uniquely associated with a symmetric incomplete block design. Williams, Patterson and John (1976) used this relationship to examine the efficiency of the designs given by Bose and Nair (1962) and Williams (1976). Recently, John and Mitchell (1977) gave a listing of optimal binary incomplete block designs obtained from an exhaustive computer search of possible designs. Using and extend-