For a graph G and a set F of connected graphs, G is said be F-free if G does not contain any member of F as an induced subgraph. We let G(3)(F) denote the set of all 3-connected F-free graphs. This paper is concerned with sets F of connected graphs such that vertical bar F vertical bar = 3 and G(3)(F) is finite. Among other results, we show that for an integer m >= 3 and a connected graph T of order greater than or equal to 4, G(3)({K-4, K-2,K-m, T}) is finite if and only if T is a path of order 4 or 5.