  We explore two distinct methods to introduce integrable defects in a family
of integrable sigma-models known as Yang-Baxter models. The first method
invokes a modified monodromy matrix encoding an integrable defect separating
two integrable systems. As an example we construct integrable defects in the
ultralocal version of the $S^2$ Yang-Baxter model or 2d Fateev sausage model.
The second method is based on the so-called "frozen" B\"acklund
transformations. Lifting the construction to the Drinfel'd double, we show how
defect matrices can be constructed for inhomogeneous Yang-Baxter models. We
provide explicit expressions for the $SU(2)$ non-split Yang-Baxter model for
this class of integrable defects.
