This article suggests a simple and unified approach to the use of auxiliary information for reducing both the sampling error and the nonresponse bias in a survey. We propose a point estimator based on calibration and a corresponding variance estimator. They are general in regard to both the sampling design and the form of the auxiliary information. The calibration procedure generates final weights which are as close as possible to specified initial weights (the design weights), while respecting known auxiliary population totals or unbiased estimates of these totals. When population totals are used, the resulting point estimators are consistent in the sense that the final weights give perfect estimates when applied to each auxiliary variable. A clear tendency in our empirical findings is that an increased auxiliary information content will reduce both variance and nonresponse bias of the point estimator. Despite some residual bias, the coverage rate of our confidence intervals comes close to a nominal 95%.