  We derive the LO DGLAP evolution equation for the full Mellin moments of the
truncated at $x_0$ first moment of the nonsinglet parton distribution. This
"moment of moment" approach allows to determine the small-$x_0$ behaviour of
the truncated first moment. We compare our predictions to results obtained from
$x-$space solutions for parton distributions with use of the Chebyshev
polynomial method and to solutions of the evolution equations for the truncated
moments proposed by other authors. The comparison is performed for different
input parametrisations for $10^{-5}\leq x_0\leq 0.1$ and $1\leq Q^2\leq 100$
${\rm GeV}^2$. We give an example of application to the determination of the
contribution to the Bjorken Sum Rule.
