E-mail is a common invitation mode for Web surveys. However, collecting e-mail addresses in another mode may raise privacy concerns among respondents. In our previous study, fewer than half the respondents provided an e-mail address. In this paper we report on an experiment to test the efficacy of asking for e-mail addresses. Respondents to the 2012 German General Social Survey (ALLBUS) who reported having Internet access at home were randomized to two groups, with one group not being asked for their e-mail address, while the other being asked. Using a mailed invitation to a follow-up Web survey, we explore the effect of this request on the subsequent response rate. We also followed up all cases (including those who reported not having Internet access at home) with a mail survey to explore the effect of adding mail in a sequential mixed-mode design. We find that asking for e-mail address does not appear to have negative effects on subsequent response. We also find that a mixed-mode design substantially increases response rates and brings the follow-up sample more in line with the ALLBUS in terms of selected demographic and attitudinal variables.