  Interesting deformations of AdS_5 x S^5 such as the gravity dual of
noncommutative SYM and Sch\"odinger spacetimes have recently been shown to be
integrable. We clarify questions regarding the reality and integrability
properties of the associated construction based on R matrices that solve the
classical Yang-Baxter equation, and present an overview of manifestly real R
matrices associated to the various deformations. We also discuss when these R
matrices should correspond to TsT transformations, which not all do, and
briefly analyze the symmetries preserved by these deformations, for example
finding Schr\"odinger superalgebras that were previously obtained as
subalgebras of psu(2,2|4). Our results contain a (singular) generalization of
an apparently non-TsT deformation of AdS_5 x S^5, whose status as a string
background is an interesting open question.
