Rule models are favored in many prediction tasks due to their interpretation using natural language and their simple presentation. When learned from data, they can provide high predictive performance, on par with more complex models. However, in the presence of incomplete input data during test time, standard rule models’ predictions are undefined or ambiguous.In this work, we consider learning compact yet accurate rule models with missing values at both training and test time, based on the notion of replacement variables. We propose a method called MINTY which learns rules in the form of disjunctions between variables that act as replacements for each other when one or more is missing. This results in a sparse linear rule model that naturally allows a trade-off between interpretability and goodness of fit while being sensitive to missing values at test time. We demonstrate the concept of MINTY in preliminary experiments and compare the predictive performance to baselines.