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The paper discusses the problem of determinising finite-state automata containing large numbers of ε-moves. Experiments with finite-state approximations of natural language grammars often give rise to very large automata with a very large number of ε-moves. The paper identifies three subset construction algorithms which treat ε-moves. A number of experiments has been performed which indicate that the algorithms differ considerably in practice. Furthermore, the experiments suggest that the average number of ε-moves per state can be used to predict which algorithm is likely to perform best for a given input automaton.