For a finite automaton, regardless whether it is deterministic or nondeterministic, Brzozowski's minimization algorithm computes the equivalent minimal deterministic finite automaton by applying reversal and power-set construction twice. Although this is an exponential algorithm because of the power-set construction, it performs well in experimental studies compared to efficient O(nlogn) minimization algorithms. Here we show how to slightly enhance Brzozowski's minimization algorithm by some sort of reachability information so that it can be applied to the following automata models: deterministic cover automata, almost equivalent deterministic finite state machines, and k-similar automata.