Elasticsearch implementation of Fuzziness

I read somewhere in the documentation that ES uses the Damerau-Levenshtein distance, or variant, for its implementation of fuzziness (at least for Fuzzy queries but this also seems to apply to the fuzziness parameter).

The thing is, my client's require that we support both the autocomplete and fuzziness functionalities, so we opted for using edge-grams and a variable fuzziness. Of course this isn't recommend because the results sometimes can be strange (since we used multiple query clauses and the same term can match twice, because of edgegrams and fuzziness).

My question is: can you somehow configure the operations allowed by fuzziness? The ideal for me would be to consider only transpositions for fuzziness, since it's the most commom mispelling and character insertion would be delt with by edgegrams.

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