The ubiquity of data transformation problems in software engineering has led to the development of bidirectional transformation techniques in a variety of application domains. Model-driven engineering (MDE) is one of those areas, where such techniques are essential to maintain the consistency between multiple coexisting and simultaneously evolving models. However, the lack of in-depth research about certain characteristics of MDE has hindered the development of effective bidirectional model transformations that are able to address realistic MDE scenarios. This dissertation tackles two of these issues: that of constrained transformation domains and least-change transformations. The first regards the transformations’ ability to take into consideration the constraints imposed by the meta-models, and is essential to achieve correctness; the second regards the transformations’ ability to control the selection of updates from among those considered correct, and is essential to achieve a predictable system. These two issues are addressed under two popular bidirectional transformation schemes: in the context of the asymmetric framework of lenses, following a combinatorial approach; and in the context of the symmetric framework of constraint maintainers, proposing a solution based on model finding. The latter was effectively deployed as Echo, a tool for model repair and transformation. The expressiveness and flexibility provided by relational logic enabled it to be used as the unifying formalism throughout this dissertation.