  In the standard example of strict deformation quantization of the symplectic
sphere $S^2$, the set of allowed values of the quantization parameter $\hbar$
is not connected; indeed, it is almost discrete. Li recently constructed a
class of examples (including $S^2$) in which $\hbar$ can take any value in an
interval, but these examples are badly behaved. Here, I identify a natural
additional axiom for strict deformation quantization and prove that it implies
that the parameter set for quantizing $S^2$ is never connected.
