  A graph $G$ has a $C_k$-decomposition if its edge set can be partitioned into
cycles of length $k$. We show that if $\delta(G)\geq 2|G|/3-1$, then $G$ has a
$C_4$-decomposition, and if $\delta(G)\geq |G|/2$, then $G$ has a
$C_{2k}$-decomposition, where $k\in \mathbb{N}$ and $k\geq 4$ (we assume $G$ is
large and satisfies necessary divisibility conditions). These minimum degree
bounds are best possible and provide exact versions of asymptotic results
obtained by Barber, K\"uhn, Lo and Osthus. In the process, we obtain asymptotic
versions of these results when $G$ is bipartite or satisfies certain expansion
properties.
