In this paper we investigate the influence of choice task complexity on the propensity to choose the status quo (SQ) alternative in discrete choice experiments. Task complexity is characterized in terms of the design dimensionality systematically varying the number of choice sets, alternatives, attributes and levels as well as the level range using 16 split samples. Moreover, we use the number of level changes across alternatives and entropy to capture further complexity effects. First, we show that the frequency of choosing the SQ and the number of those respondents who always stay at the SQ varies across designs. Using a count data model and a binary logit we observe that both figures are particularly influenced by the number of alternatives. By interacting the alternative-specific constant of the SQ with our complexity measures in a conditional and random parameter logit, we then find that the probability to choose the SQ decreases with the number of alternatives and with designs having three attribute levels. The propensity to stay at the SQ, however, increases with higher values of entropy, more choice sets, and designs with a wider level range. Significant effects of socio-demographic characteristics on SQ choices are present in all our models.