The response bias hypothesis specifies that the predictive capacity of a predictor should be enhanced by controlling for the effects of bias on the predictor variable, in particular, socially desirable responding (SDR) bias. To-date, the vast majority of the SDR research in the area, which is principally personality related, has failed to support the response bias hypothesis, as SDR suppressor effects have not been observed. Consequently, it has been contended that SDR is not a problem for self-report measurement, that SDR measures may themselves be indicators of trait variance, and that it was likely impossible to determine whether an elevated SDR score reflected a trait or response bias. However, in contrast to personality, intelligence is an area within which comparisons between subjective scores (self-reported) and objective scores (task-based) can be made. Consequently, the purpose of this investigation was to test the response bias hypothesis (N = 253) with self-report measures of intellectual and emotional intelligence (SRIQ and SREI) and task-based measures of intellectual and emotional intelligence (TBIQ and TBEI), in conjunction with a multi-dimensional measure of SDR (Balanced Inventory of Desirable Responding; BIDR). The percentage of variance accounted for in TBIQ by SRIQ, and in TBEI by SREI, increased by 1% and 2.1%, respectively, when SDR was included in the model. The 1% to 2.1% increases in criterion (concurrent) validity were interpreted as practically significant, based on previously published simulation work. Finally, it was concluded that self-report measures may be non-negligibly influenced by individual differences in SDR, and that the BIDR may possess some validity as an indicator of individual differences in socially desirable responding.