This paper describes improved methods for XTR key representation and parameter generation (Lenstra et al., 2000). If the field characteristic is properly chosen, the size of the XTR public key for signature applications can be reduced by a factor of three at the cost of a small one time computation for the recipient of the key. Furthermore, the parameter set-up for an XTR system can be simplified because the trace of a proper subgroup generator can, with very high probability, be computed directly, thus avoiding the probabilistic approach from Lenstra. These non-trivial extensions further enhance the practical potential of XTR