  Serre's strong conjecture, now a theorem of Khare and Wintenberger, states
that every two-dimensional continuous, odd, irreducible mod $p$ Galois
representation $\rho$ arises from a modular form of a specific minimal weight
$k(\rho)$, level $N(\rho)$ and character $\epsilon(\rho)$. In this short paper
we show that the minimal weight $k(\rho)$ is equal to a notion of minimal
weight inspired by the recipe for weights introduced by Buzzard, Diamond and
Jarvis. Moreover, using the Breuil-M\'{e}zard conjecture we show that both
weight recipes are equal to the smallest $k \geq 2$ such that $\rho$ has a
crystalline lift of Hodge-Tate type $(0,k-1)$.
