The effects on Rasch measurement of both response underfit (noise) and overfit (mutedness or superuniformity) are described and illustrated. Misfit is identified by mean-square fit statistics. Person separation and reliability are shown to be deceptive indicators of measurement effectiveness when some items exhibit marked overfit. Theoretical considerations are confirmed by adding simulated items of known fit to a core of empirically observed Knox Cube Test responses of 34 children. Measure effectiveness, model fit, and utility must be considered together when deciding which subset of data is most informative for the particular task at hand. One subset of data may be most informative for item calibration, and another for reporting person measures based on the precalibrated items. (Contains four figures and two references.) (Author/SLD)