In this paper balanced optimal fractional factorial designs of 2mseries which allow the estimation of the general mean, main effects and two factor interactions are described. Such designs are presented for eachmwith 4 ≤m≤ 6, and for a range of practical values ofN, whereNdenotes the total number of level-combinations. The covariance matrices of the estimates of the effects are also presented for each design, with a set of simple formulae for calculating these estimates.