A dominating set in a graph $$G$$ G is a set $$S$$ S of vertices such that every vertex outside $$S$$ S has a neighbor in $$S$$ S ; the domination number $$\gamma (G)$$ γ ( G ) is the minimum size of such a set. The independent domination number, written $$i(G)$$ i ( G ) , is the minimum size of a dominating set that also induces no edges. Henning and Southey conjectured $$i(G)/\gamma (G) \le 6/5$$ i ( G ) / γ ( G ) ≤ 6 / 5 for every cubic (3-regular) graph $$G$$ G with sufficiently many vertices. We provide an infinite family of counterexamples, giving for each positive integer $$k$$ k a 2-connected cubic graph $$H_k$$ H k with $$14k$$ 14 k vertices such that $$i(H_k)=5k$$ i ( H k ) = 5 k and $$\gamma (H_k)=4k$$ γ ( H k ) = 4 k .