  We determine rational Kisin modules associated with two-dimensional,
irreducible, crystalline representations of
$\mathrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$ of Hodge-Tate weights $0,
k-1$. If the slope is larger than $\lfloor \frac{k-1}{p} \rfloor$, we further
identify an integral Kisin module, which we use to calculate the semisimple
reduction of the Galois representation. In that range, we find that the
reduction is constant, thereby improving on a theorem of Berger, Li, and Zhu.
