Following a brief review of the "two-level (tunneling) systems" model of the low-temperature properties of amorphous solids ("glasses"), we ask whether it is in fact the unique explanation of these properties as is usually assumed, concluding that this is not necessarily the case. We point out that (a) one specific form of the model is already experimentally refuted and (b) that a definitive test of the model in its most general form, while not yet carried out, would appear to be now experimentally feasible.