  We show that every $2$-connected cubic graph $G$ has a cycle double cover if
$G$ has a spanning subgraph $F$ such that (i) every component of $F$ has an
even number of vertices (ii) every component of $F$ is either a cycle or a
subdivision of a Kotzig graph and (iii) the components of $F$ are connected to
each other in a certain general manner.
