Processing implemented by a method and apparatus herein advantageously improves the quality of measurements performed by a wireless device (36), by ensuring that the device (36) measures its serving cell over at least as large of a bandwidth as the bandwidth over which it measures neighbor cells. Such processing specifically includes identifying, for each of a plurality of neighbor cells, a measurement bandwidth over which the wireless device (36) is to perform measurements of that cell. Processing then entails selectively initiating handover of the wireless device (36) from a serving cell to one of the neighbor cells, depending on how many of those neighbor cells have a measurement bandwidth larger than that of the serving cell. Thus, contrasted with traditional performance-based handovers that are conducted based on the strength of already made reference signal measurements, handover herein is performed based on the bandwidth(s) over which such measurements will be performed in the future.