Consider a group divisible (GD) design with parameters v, b, r, k, λ₁, λ₂. From apractical point of view on optimality, GD designs with λ₂=λ₁-1 are partly characterized. Furthermore, all the GD designs satisfying rk-λ₂v_??_4 and r-λ₁_??_4 aresearched, where rk-λ₂v and r-λ₁ are eigenvalues ofNN' other than rk for the incidente matrix N of the design. These produce more efficient GD designs.