Snarks with Special Spanning Trees

Let G be a cubic graph which has a decomposition into a spanning tree T and a 2-regular subgraph C, i.e. E(T)E(C)=E(G) and E(T)E(C)=empty set. We provide an answer to the following question: which lengths can the cycles of C have if G is a snark? Note that T is a hist (i.e. a spanning tree without a vertex of degree two) and that every cubic graph with a hist has the above decomposition.