For any integer r > 1, an r- trestle of a graph G is a 2-connected spanning subgraph F with maximum degree Δ( F) ≤ r. A graph G is called K- free if G has no K as an induced subgraph. Inspired by the work of Ryjáček and Tkáč, we show that every 2-connected K-free graph has an r-trestle. The paper concludes with a corollary of this result for the existence of k-walks.