We start with a basic optimization objective (Mikolov et al., 2013b) and introduce several meaningful and intuitive constraints that are equivalent or closely related to previously proposed methods <cite>(Faruqui and Dyer, 2014</cite>; Xing et al., 2015) . Our framework provides a more general view of bilingual word embedding mappings, showing the underlying connection between the existing methods, revealing some flaws in their theoretical justification and providing an alternative theoretical interpretation for them.