We elaborate on the class of deformed T-dual (DTD) models obtained by first adding a topological term to the action of a supercoset sigma model and then performing (non-abelian) T-duality on a subalgebra (g) over tilde of the superisometry algebra. These models inherit the classical integrability of the parent one, and they include as special cases the socalled homogeneous Yang-Baxter sigma models as well as their non-abelian T-duals. Many properties of DTD models have simple algebraic interpretations. For example we show that their (non-abelian) T-duals - including certain deformations - are again in the same class, where (g) over tilde gets enlarged or shrinks by adding or removing generators corresponding to the dualised isometries. Moreover, we show that Weyl invariance of these models is equivalent to (g) over tilde being unimodular; when this property is not satisfied one can always remove one generator to obtain a unimodular (g) over tilde, which is equivalent to (formal) T-duality. We also work out the target space super fields and, as a by-product, we prove the conjectured transformation law for Ramond-Ramond (RR) fields under bosonic non-abelian T-duality of supercosets, generalising it to cases involving also fermionic T-dualities.