Most of the speedup was not the result of using an algorithm optimized for sorted data-an improvement to the algorithm for adding strings in Carrasco and Forcada (2002) consisting in avoiding unnecessary cloning of prefix states (as described in section 3.2 and mentioned on page 215 in Carrasco and Forcada [2002] as a suggestion from one of Carrasco and Forcada's reviewers) was 3.12 and respectively 2.35 times faster than the original algorithm.
the new algorithm is still the fastest.