Rising nonresponse rates in social surveys make the issue of nonresponse bias contentious. There are conflicting messages about the importance of high response rates and the hazards of low rates. Some articles (e.g. Groves and Peytcheva, 2008) suggest that the response rate is in general not a good predictor of survey quality. Equally, it is well known that nonresponse may induce bias and increase data collection costs.  We go back in the history of the literature of nonresponse and suggest a possible reason to the notion that even a rather small nonresponse rate makes the quality of a survey debatable. We also explore the relationship between nonresponse rate and bias, assuming non-ignorable nonresponse and focusing on estimates of totals or means. We show that there is a ‘safe area’ enclosed by the response rate on the one hand and the correlation between the response propensity and the study variable on the other hand; in this area, 1) the response rate does not greatly affect the nonresponse bias and 2) the nonresponse bias is small.