  We describe a unifying framework for the systematic construction of
integrable deformations of integrable $\sigma$-models within the Hamiltonian
formalism. It applies equally to both the `Yang-Baxter' type as well as `gauged
WZW' type deformations which were considered recently in the literature. As a
byproduct, these two families of integrable deformations are shown to be
Poisson-Lie T-dual of one another.
