In 1982 Laborde, Payan and Xuong Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982) 173-177 (Teubner-Texte Math., 59 1983) conjectured that every digraph has an independent detour transversal (IDT), i.e. an independent set which intersects every longest path. Havet Stable set meeting every longest path, Discrete Math. 289 (2004) 169-173 showed that the conjecture holds for digraphs with independence number two. A digraph is p-deficient if its order is exactly p more than the order of its longest paths. It follows easily from Havet’s result that for p = 1, 2 every p-deficient digraph has an independent detour transversal. This paper explores the existence of independent detour transversals in 3-deficient digraphs.