We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters () and infinite dimensional unknown functions (). Our proposal is to approximate with a sieve and to estimate and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of is consistent with a rate faster than under certain metric; (ii) the estimator of is √ consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function.