Recently the Multi-Level algorithm was introduced as a general purpose
solver for the solution of steady state Markov chains.
In this paper we consider the performance of the Multi-Level
algorithm for solving Nearly Completely Decomposable (NCD) Markov chains,
for which special-purpose iterative aggregation/disaggregation
algorithms such as the Koury-McAllister-Stewart (KMS) method have been 
developed that can exploit the decomposability of the the Markov chain.
We present experimental results indicating that
the general-purpose Multi-Level algorithm  
is competitive, and can be significantly faster 
than the special-purpose KMS algorithm when Gauss-Seidel and 
Gaussian Elimination are used for solving the individual blocks.