Retrospective demographic surveys typically collect substantial information about child health. This information is often collected for all children born during a specified period. For women with several young children, the interview can become quite long. To shorten the interview, some surveys have asked child health questions only for the last child born. However, data on the last birth may be biased because last children have a younger age distribution and have longer subsequent birth intervals than does the average child. In this paper, we propose an alternative approach to collecting child health data - that child health questions be asked only for a child chosen randomly from among the respondent's children younger than age five. This alternative has the advantage of keeping the interview shorter but does not lead to biased information.