  In a hidden Markov model, the underlying Markov chain is usually hidden.
Often, the maximum likelihood alignment (Viterbi alignment) is used as its
estimate. Although having the biggest likelihood, the Viterbi alignment can
behave very untypically by passing states that are at most unexpected. To avoid
such situations, the Viterbi alignment can be modified by forcing it not to
pass these states. In this article, an iterative procedure for improving the
Viterbi alignment is proposed and studied. The iterative approach is compared
with a simple bunch approach where a number of states with low probability are
all replaced at the same time. It can be seen that the iterative way of
adjusting the Viterbi alignment is more efficient and it has several advantages
over the bunch approach. The same iterative algorithm for improving the Viterbi
alignment can be used in the case of peeping, that is when it is possible to
reveal hidden states. In addition, lower bounds for classification
probabilities of the Viterbi alignment under different conditions on the model
parameters are studied.
