In this talk we will discuss integrable deformations of the Principal Chiral Model (PCM) plus Wess-Zumino (WZ) term. Adding a WZ term to the PCM preserves integrability, as do the Yang-Baxter deformations. Both also preserve 1-loop renormalisability, but modify the RG flow in different ways. After deriving a cohomological condition that should be satisfied for both to be done simultaneously, we will give the expression for the deformed action and discuss its integrability. We will also briefly explore how this construction fits into various organisational frameworks such as E-models, 4-d Chern-Simons and non-abelian T-duality.