Apparatus and techniques for laser-processing workpieces can be improved, and new functionalities can be provided. Some embodiments discussed relate to processing of workpieces in a manner resulting in enhanced accuracy, throughput, etc. Other embodiments relate to realtime Z-height measurement and, when suitable, compensation for certain Z-height deviations. Still other embodiments relate to modulation of scan patterns, beam characteristics, etc., to facilitate feature formation, avoid undesirable heat accumulation, or otherwise enhance processing throughput. A great number of other embodiments and arrangements are also detailed.