A network node receiving a preference for a power optimized configuration for a user equipment (UE) can in response change the UE's minimization of drive test (MDT) configuration to conserve UE power. For example, this change can be from immediate reporting of MDT measurements to connected mode logging MDT measurements or no reporting of MDT measurements; or to a longer interval for reporting them, or to drop the reporting of available location information with MDT measurements. Other teachings have actions by the UE, autonomous of the network, to conserve power. A UE receiving a MDT configuration having an MDT measurement reporting or logging interval, and also one or both of a discontinuous reception or paging configuration having a DRX/paging interval can adapt the MDT configuration autonomously of the network to conserve its battery power. For example, the UE can change the MDT measurement reporting/logging interval to be equal to or shorter than the DRX/paging interval, or it can ignore or reject the MDT configuration.