Decompositions make it possible to investigate whether gaps between groups in certain outcomes would remain if groups had comparable characteristics. In practice, however, such a counterfactual comparability is difficult to establish in the presence of lacking common support, functional-form misspecification, and insufficient sample size. In this article, the authors show how decompositions can be undermined by these three interrelated issues by comparing the results of a regression-based Kitagawa-Blinder-Oaxaca decomposition and matching decompositions applied to simulated and real-world data. The results show that matching decompositions are robust to issues of common support and functional-form misspecification but demand a large number of observations. Kitagawa-Blinder-Oaxaca decompositions provide consistent estimates also for smaller samples but require assumptions for model specification and, when common support is lacking, for model-based extrapolation. The authors recommend that any decomposition benefits from using a matching approach first to assess potential problems of common support and misspecification.