The versatility of the brute force orientation of polar asymmetric top molecules in a molecular beam has been investigated. In symmetric top molecules the electric field only mixes free rotor basis functions with different J but equal K and M values, but in asymmetric top molecules the mixing includes K, because of the asymmetry, in addition to field-induced J-mixing. This distinction is important with respect to the orientation behavior. For asymmetric top molecules all Stark curves for different J-states and different K-values, but equal M, in the corresponding symmetric eigenbasis, feature avoided crossings. Dependent on the velocity with which the molecules pass through the orientation field, these avoided crossings will be traversed adiabatically or nonadiabatically. For near-symmetric top molecules, such as iodobenzene, the crossings will in general be nonadiabatic, and, as expected, the behavior is similar to that of the corresponding symmetric top. If the crossings are adiabatic, the orientation behavior can be drastically different from the behavior of the corresponding symmetric top molecule. A strong asymmetry need not always be prohibitive in attaining a perceptible degree of orientation, as is demonstrated by the case of water.