Recent experiments have demonstrated the efficacy of orienting low rotational states of a linear polar molecule in a static electric field, epsilon(S), or aligning a molecule (polar or not) in an intense nonresonant laser field, epsilon(L). We present theoretical results showing that the combined action of epsilon(S) and epsilon(L) can markedly sharpen orientation, particularly by introducing a pseudo-first-order Stark effect for tunneling doublets created by the polarizability interaction. Also, if epsilon(S) and epsilon(L) are not collinear, the molecular axis can be localized with respect to phi as well as theta, since M states as well as J states undergo hybridization. Another benefit is a means to eliminate "wrong way orientation" which otherwise occurs for "low-field seeking" states.