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

On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring