In this paper several modifications of two methods for parameter reduction of Hidden Markov Models by state tying are described. The two methods represent a data driven clustering triphone states with a bottom up algorithm [3, 9], and a top down method growing decision trees for triphone states [2, 10]. We investigate several aspects of state tying as the possible reduction of the word error rate by state tying, the consequences of different distance measures for the data driven approach and modi_cations of the original decision tree approach such as node merging. The tests were performed on the test corpora for the 5 000 word vocabulary of the WSJ November 92 task and on the evaluation corpora for the 3 000 word VERBMOBIL '95 task. The word error rate by state tying was reduced by 14% for the WSJ task and by 5% for the VERBMOBIL task.