If the scintillator response to a hadronic shower in a semi-infinite uniform calorimeter structure is S relative to the electronic response, then, where E is the incident hadron energy, f em is the electronic shower fraction, and h/e is the hadron/electron response ratio. If there is also a simultaneous readout with a different h/e, say a Cherenkov signal C, then a linear combination of the two signals provides an estimator of E that is proportional to the incident energy and whose distribution is nearly Gaussian-even though the S and C distributions are non-linear in E, wide, and skewed. Since an estimator of f em is also obtained, it is no longer a stochastic variable. Much of the remaining resolution variance is due to sampling fluctuations. These can be avoided in a homogeneous calorimeter. The energy resolution depends upon the contrast in h/e between the two channels. h/e is small in the Cherenkov channel. Mechanisms that increase h/e in sampling calorimeters with organic scintillator readout are not available in a homogeneous inorganic scintillator calorimeter. The h/e contrast is very likely too small to provide the needed energy resolution.1 Technically, a power-law fit finds a = (1 − h/e )E 1−m 0 . Since 1 − m is small and the scale energy E 0 is close to 1 GeV for pion-induced cascades, the distinction is minor: h/e ≈ 1 − a. A similar distinction occurs when other parameterizations are used. h/e itself cannot be isolated.