There are many situations in which physical interaction with real-world objects is not possible - for example, museums contain many objects or artefacts which are too fragile or expensive for the public to handle. Augmented Reality (AR) has the potential to offer an alternative in these situations, but most of our current interactions with virtual objects in AR tend to be indirect. Tangible AR allows for natural movement, but we rarely manipulate or control virtual objects beyond that in the way we do their physical counterparts. To address this problem, we propose that a more natural approach to interacting with tangible AR be introduced. We present a prototype that allows users to physically orientate virtual objects so that they 'snap' together in order to complete a '3D AR Puzzle', and show that introducing 'responsive virtual objects' for tangible AR is a promising first step towards more natural interactions.