In modern automatic speech recognition systems, it is standard practice to cluster several logical hidden Markov model states into one physical, clustered state. Typically, the clustering is done such that logical states from different phones or different states can not share the same clustered state. In this paper, we present a collection of experiments that lift this restriction. The results show that, for Aurora 2 and Aurora 3, much smaller models perform as least as well as the standard baseline. On a TIMIT phone recognition task, we analyze the tying structures introduced, and discuss the implications for building better acoustic models.