  We consider perturbative expansions in theories with an infrared cutoff
$\lambda$. The infrared sensitive pieces are defined as terms nonanalytic in
the infinitesimal $\lambda^2$ and powers of this cutoff characterize the
strength of these infrared contributions. It is argued that the sum over the
initial and final degenerate ( as $\lambda \to 0$) states which is required by
the Kinoshita - Lee - Nauenberg theorem eliminates terms of order $\lambda^0$
and $\lambda^1$. However, the quadratic and higher order terms in general do
not cancel. This is investigated in simple examples of KLN cancellations, of
relevance to the inclusive decay rate of a heavy particle, at the one loop
level.
