In this paper, we present a new Deterministic Finite Automata (DFA) minimization algorithm. The algorithm is incremental – it may be halted at any time, yielding a partially-minimized automaton. All of the other (known) minimization algorithms have intermediate results which are not useable for partial minimization. Since the first algorithm is easily understood but inefficient, we consider three practical and effective optimizations. The first two optimizations do not affect the asymptotic worst-case running time – though they perform well on a large class of automata. The third optimization yields an quadratic-time algorithm which is competitive with the previously known ones.