Two distinct types of models are used for handling nonresponse in survey sampling theory. In a response (or quasi-randomization) model, the propensity of survey response is modeled as a random process, an additional phase of sample selection. In a parametric (or superpopulation) model, the survey data are themselves modeled. These two models can be used simultaneously in the estimation of a population mean so that one provides some protection against the potential for failure in the other. Two different estimators are discussed in this article. The first is a regression estimator that is both unbiased under the parametric model and nearly quasi-design unbiased under the response model. The second is a direct expansion estimator with imputed missing values. The imputed values are such that the estimator is both nearly quasi-design unbiased and unbiased under the combination of the parametric model and the original sampling design. The article includes a discussion of variance estimation with the goal of simultaneously estimating quasi-design mean squared error and either parametric model variance or combined (parametric model and original design) variance.