In personality and attitude measurement, the presence of acquiescent responding can have an impact on the whole process of item calibration and test scoring, and this can occur even when sensible procedures for controlling acquiescence are used. This paper considers a bidimensional (content acquiescence) factor-analytic model to be the correct model, and assesses the effects of fitting unidimensional models to theoretically unidimensional scales when acquiescence is in fact operating. The analysis considers two types of scales: non-balanced and fully balanced. The effects are analysed at both the calibration and the scoring stages, and are of two types: bias in the item/respondent parameter estimates and model/person misfit. The results obtained theoretically are checked and assessed by means of simulation. The results and predictions are then assessed in an empirical study based on two personality scales. The implications of the results for applied personality research are discussed.