Sufficient conditions are derived for the determination of E-optimal designs in the classD (v,b 1 ,b 2 ,k 1 ,k 2 ) of incomplete block designs forv treatments in b 1 blocks of size k 1 each and b 2 blocks of size k 2 each. Some constructions for E-optimal designs that satisfy the sufficient conditions obtained here are given. In particular, it is shown that E-optimal designs inD (v,b 1 ,b 2 ,k 1 ,k 2 ) can be constructed by augmenting b 2 blocks, with k 2 - k 1 extra plots each, of a BIBD(v,b = b 1 + b 2 ,k 1 ,λ) and GDD(v,b =b 1 + b 2 ,k 1 ,λ 1 ,λ 2 ). It is also shown that equireplicateE -optimal designs in D(v,b 1 ,b 2 ,k 1 ,k 2 ) can be constructed by combining disjoint blocks of BIBD(v,b,k 1 ,λ) and GDD(v,b,k 1 ,λ 1 ,λ 2 ) into larger blocks. As applications of the construction techniques, several infinite series of E-optimal designs with small block sizes differing by at most two are given. Lower bounds for the A-efficiency are derived and it is found that A-efficiency exceeds 99% for v 10, and at least 97.5% for 5 v < 10.