A generalization of ordered statisics decoding (OSD) is obtained 
for the intersymbol interference (ISI) channel. The OSD is a powerful 
reliability-based decoder, that utilizes symbols that have been 
ordered according to their reliability. The OSD focuses on highly
reliable symbols, which are the ones more likely to have been 
recieved correctly. Impressive decoding gains are observed for
ISI channels, comparable to those observed for the memoryless 
AWGN channel. Analytic estimates for the symbol error probabilities 
with respect to reliability ordering, are given. The distribution 
of the symbol reliabilities (obtained from a (windowed) Max-Log-Map 
decoder) is derived. We also consider two other important aspects 
related to the OSD. Firstly, an OSD enhancement known as the 
Box-and-Match (BMA) technique, is generalized for the ISI channel. 
The BMA enchancement improves the OSD error correcting capability 
with marginal complexity increase. Secondly, codeword optimality 
tests are generalized for ISI channels. These so-called optimality 
tests are used to reduce decoding complexity of OSD-like algorithms.