Low-temperature zero-field muon spin relaxation spectra from several d
isordered magnetic materials show static-field relaxation behavior tha
t cannot be properly represented by the Gaussian or Lorentzian distrib
utions commonly used in the analysis of such data (Kubo-Toyabe relaxat
ion). In the case oi CeCu0 2Ni0.8Sn, a Gaussian distribution of second
moments, convoluted with a Gaussian form of field distribution, produ
ces a closed-form modified Kubo-Toyabe relaxation function that fits t
he data well. Its characteristic feature is a shallow polarization min
imum before recovery to the 1/3 asymptote. Any microscopic model that
reproduces such shallow static Kubo-Toyabe relaxation must do so by ge
nerating an excess of low-field sites.