We have previously shown that the material removal rate scales linearly with pulse rate up to 15 kHz for pulsed UV-laser ablation of polymers, giving the potential for substantial gains in processing speeds in ablative micromachining using high-pulse-rate UV sources such as frequency-doubled copper vapor lasers and frequency-quadrupled diode-pumped solid-state lasers. These rapid processing speeds can be effectively utilized in direct-write UV-laser micromachining including trepanning. In this paper we present studies of machining rates for trepanning of a strongly absorbing polymer (PETG), and a weakly absorbing polymer (PMMA), aimed at establishing optimum conditions of pulse rate, linear write speed (laser spot overlap) and laser fluence for maximum machining rates and high quality of the machined structure using a high-pulse- rate (5 kHz) UV-CVL. For fixed fluence and pulse rate, machining rates for PETG are found to be independent of write speed in trepanning, however for PMMA machining rates increase for decreasing write speed (increasing laser spot overlap) where cumulative heating leads to enhanced dynamic etch rates. In the latter case, while reduced machining times can be achieved for high spot overlaps, this is generally at the expense of significant degradation in finish quality of the machined structure.