  We analyze a toy model which has a structure similar to that of the recently
found QCD evolution equations, but without transverse dimensions. We develop
two different but equivalent methods in order to compute the leading-order and
next-to-leading order Pomeron loop diagrams. In addition to the leading-order
result which has been derived from Mueller's toy model~\cite% {Mueller:1994gb},
we can also calculate the next-to-leading order contribution which provides the
$(\alpha_{s}^{2}\alpha Y)$ correction. We interpret this result and discuss its
possible implications for the four-dimensional QCD evolution.
