Locating faults in spreadsheets can be difficult. Therefore, tools supporting the localization of faults are needed. This paper presents a novel dependency-based model that can be used in Model-based software debugging (MBSD). This model allows improvements of the diagnostic accuracy while keeping the computation times short. In an empirical evaluation, we show that dependency-based models of spreadsheets whose value-based models are often not solvable in an acceptable amount of time can be solved in less than one second. Furthermore, the amount of diagnoses is reduced by 15 % on average when using the novel instead of the original dependency-based model.