  The so-called "optimal filter" analysis of a microcalorimeter's x-ray pulses
is statistically optimal only if all pulses have the same shape, regardless of
energy. The shapes of pulses from a nonlinear detector can and do depend on the
pulse energy, however. A pulse-fitting procedure that we call "tangent
filtering" accounts for the energy dependence of the shape and should therefore
achieve superior energy resolution. We take a geometric view of the
pulse-fitting problem and give expressions to predict how much the energy
resolution stands to benefit from such a procedure. We also demonstrate the
method with a case study of K-line fluorescence from several 3d transition
metals. The method improves the resolution from 4.9 eV to 4.2 eV at the Cu
K$\alpha$ line (8.0keV).
