Free strings on backgrounds such as AdS3xS3xT4 and AdS3xS3xS3xS1 can be described by integrable sigma models, which admit a very rich landscape of integrable deformations. In this talk I will focus on TsT, trigonometric and elliptic deformations which preserve some amount of supersymmetries and interpolate between well-known integrable setups. I will present the deformed geometry and check that the S-matrix encoding the scattering of excitations on the string worldsheet is compatible with factorisation.