An extensive CRAY-computer-based simulator using the propagating beam method for the accurate evaluation of the performance of optical fiber up-tapers is discussed. Up-tapers with and without straight tips and with arbitrary index profiles and tapering functions can be evaluated. Results of the evaluation of various 1.5-cm-long optical up-tapers followed by a straight tip and drawn from special preforms with various index profiles are quite encouraging. They show that beam expansion ratios in the range of 5-10 are feasible with a corresponding insertion loss per taper of less than 0.01-0.025 dB. Tapers shorter than 1.5 cm with insertion loss in the same range are also feasible but have slightly smaller beam expansion ratios. >