Motivated by Haq et al. (2017), Mohamed et al. (2018) and some recent developments for the estimation of finite population mean, we propose a new design based imputation procedure for the imputation of missing values by applying some sensible constraints on the study and the auxiliary variables, respectively. The proposed design is considered under two assumptions: (i) the study variable is a non-sensitive variable that the measurements on the study variable do not create any embarrassment during personal interview and (ii) the study variable is a sensitive variable where the measurement errors are introduced due to some untruthful responses. These measurement errors are minimized up to some extend by using the scrambling response models. The proposed imputed values are obtained by the dual use of the auxiliary information leading to a consistent estimator that seems like the linear regression method of imputation. Expressions for the mean square error (MSE) are obtained up to the first order approximation. Finally, simulation studies are carried out in favor of the proposed estimators.