We consider the problem of parameter estimation with auxiliary information, where the auxiliary information takes the form of known moments. Calibration estimation is a typical example of using the moment conditions in sample surveys. Given the parametric form of the original distribution of the sample observations, we use the estimated importance sampling of Henmi, Yoshida and Eguchi (2007) to obtain an improved estimator. If we use the normal density to compute the importance weights, the resulting estimator takes the form of the one-step exponential tilting estimator. The proposed exponential tilting estimator is shown to be asymptotically equivalent to the regression estimator, but it avoids extreme weights and has some computational advantages over the empirical likelihood estimator. Variance estimation is also discussed and results from a limited simulation study are presented.