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In this paper we consider the problem of deriving upper bounds on the number of state variables required for an n-state universal asynchronous state assignment (i.e., a state assignment which is valid for any n-state asynchronous sequential function). We will consider a special class of state assignments called SST assignments which were first derived by Liu  and later extended by Tracey . In these assignments all variables which must change in a given transition are allowed to change simultaneously without critical races. The best universal bound known so far has been developed by Liu and requires 2so-1 state variables, where S0 = [log2n], n being the number of states, and [x] being the least integer > x. We shall show how this bound can be substantially improved. We further show that, by generalizing the state assignment to allow multiple codings for states, the bounds can be still further improved.