  We perform fits of $\Lambda_{\rm QCD}$ and the gluon fragmentation function
$D(x,Q)$ at initial scale $Q_0 \gg\Lambda_{\rm QCD}$ to charged light hadron
momentum spectra data by evolving in the Modified Leading Logarithm
Approximation. Without additional assumptions, we achieve a good description of
the available data for $\xi=\ln(1/x)$ up to and around the Gaussian peak, and
values of $\Lambda_{\rm QCD}$ acceptably close to those in the literature. In
particular, we find that this procedure describes the position of the peak,
and, in contrast to the Limiting Spectrum, also the normalization.
