A common problem faced by statistical institutes is that data may be missing from collected data sets. The typical way to overcome this problem is to impute the missing data. The problem of imputing missing data is complicated by the fact that statistical data collected by statistical institutes often have to satisfy certain edit rules, which for numerical data usually take the form of linear restrictions. Standard imputation methods for numerical data as described in the literature generally do not take such linear edit restrictions on the data into account. Hot-deck imputation techniques form a well-known class and relatively simple to apply class of imputation methods. In this paper we extend this class of imputation methods so that linear edit restrictions are satisfied.