A-optimal designs for comparing v test treatments with a control in b blocks of size k each are considered. Several series of A-optimal designs are given when the parameters are in the range 2 ≤ k ≤ 8, k ≤ v ≤ 30, v ≤ b ≤ 50. A-optimal designs in blocks of size 2 are extensively studied through a combination of theoretical results and numerical investigations. Tables of approximately A-optimal designs are given when A-optimal designs are not easily available for the case k = 2.