Let δ(H) be the minimum degree of the graphH. We prove that a graphHof ordernwith δ(H) ⩾ (2n−1)/3 contains any graphGof order at mostnand maximum degree Δ(G) ⩽ 2 as a subgraph, and this bound is best possible. Furthermore, this result settles the case Δ(G) = 2 of the well‐known conjecture of Bollobás, Catlin and Eldridge on packing two graphs with given maximum degree.