Procedures based on the Generalized Method of Moments (GMM) are basic tools in modern econometrics. In most cases, the theory available for making inference with these procedures is based on first order asymptotic theory. It is well-known that the (first order) asymptotic distribution does not provide accurate p-values and confidence intervals in moderate to small samples. Moreover, in the presence of small deviations from the assumed model, p-values and confidence intervals based on classical GMM procedures can be drastically affected (nonrobustness). Several alternative techniques have been proposed to improve the accuracy of GMM procedures. These alternatives address either the first order accuracy of the approximations (information and entropy econometrics (IEE)) or the nonrobustness (Robust GMM estimators and tests). A new procedure which combines robustness properties and accuracy in small samples is proposed. Specifically, IEE techniques are combined with robust methods obtained by bounding the original orthogonality function. This leads to new robust estimators and tests in moment condition models with excellent finite sample accuracy. Finally, the accuracy of the new statistic is illustrated with Monte Carlo simulations for three models on overidentifying moment conditions.