Deformation quantization in principle allows energy distributions which require that some quantum states occur with negative probability; an ob- servable distribution is one where the probability of every pure quantum state is non-negative. The quantum uncertainty of the original distribu- tion is the uncertainty in the energy distribution of these quantum states. Quantization by algebraic deformation always produces not one but a family of quantizations one of which is usually in some natural way se- lected by the physical problem. We propose here and illustrate in the case of the simple harmonic oscillator an analytic selection principle: the quantum uncertainty of an observable probability distribution of energies must be no greater than that of the original distribution. In the case of the simple harmonic oscillator this allows only the Groenewold-Moyal quantization. Using identities on Laguerre polynomials arising from the quantization procedure itself we exhibit `enough' observable distributions which combine to give the result.