  A cycle cover of a graph is a collection of cycles such that each edge of the
graph is contained in at least one of the cycles. The length of a cycle cover
is the sum of all cycle lengths in the cover. We prove that every bridgeless
cubic graph with $m$ edges has a cycle cover of length at most $212/135 \cdot m
\ (\approx 1.570 m)$. Moreover, if the graph is cyclically $4$-edge-connected
we obtain a cover of length at most $47/30 \cdot m \approx 1.567 m$.
