Let {p(x, θ): θ∈Θ} be a family of densities where θ=(θ1,θ2), being θ1 ∈ Θ1 ak-dimensional parameter of interest, θ2 ∈ Θ2 a nuisance parameter and Θ=Θ1×Θ2. To estimate θ1, vector estimating equations g(x,θ1)=(g1(x,θ1),...,gk(x,θ1))=0 are considered. The standardized form of g(x,θ1) is defined as gs=(Eθ(∂g/∂θ′1))−1g. Then, within the classG 1 of unbiased equations (i.e. satisfying Eθ(g)=0 (θ∈Θ)), an equationg *=0 is said to be optimum if the covariance matrices ofg s andg s * are such that \( \sum _{g_s g_s } - \sum _{g_s^ * g_s^ * } \) is non-negative definite for allg∈ G 1 and θ∈Θ. Sufficient conditions for optimality are discussed and, in particular, conditions for the optimality of the maximum conditional likelihood equation are analyzed. Special attention is given to non-regular cases. In addition, measures of the information about θ1 contained in an estimating equation are presented and a Rao-Blackwell theorem is given.