The ultra-fast control of large polyatomic molecules in the gas and condensed phases entails working with a randomly oriented ensemble. During the short control period, little reorientation may occur especially for cases in the condensed phases. This paper addresses the degree to which all members of the ensemble may be simultaneously controlled with respect to their internal motion by a single laser pulse. It is shown that all members of the ensemble are fully controllable if any one member is. Numerical optimal control simulations also show that excellent quality full ensemble control can be achieved even with reasonable constraints placed on the control fields. Although the full ensemble may be controlled to a high degree, the control mechanism is likely to differ for each ensemble member.