Cluster sample surveys of health and nutrition in rural areas of developing countries frequently utilize the EPI (Expanded Programme on Immunization) method of selecting households where complete enumeration and systematic or simple random sampling (SRS) is considered impractical. The first household is selected by choosing a random direction from the centre of the community, counting the houses along that route, and picking one at random. Subsequent households are chosen by visiting that house which is nearest to the preceding one. Using a computer, and data from a survey of all children in 30 villages in Uganda, we simulated the selection of samples of size 7, 15 and 30 children from each village using SRS, the EPI method, and four different modifications of the EPI method. The choice of sampling scheme for households had very little effect on the precision or bias of estimates of prevalence of malnutrition, or of recent morbidity, with EPI performing as well as SRS. However, the EPI scheme was inefficient and showed bias for variables relating to child care and for socioeconomic variables. Two of the modified EPI schemes (taking every fifth house and taking separate EPI samples in each quarter of the community) performed in general much better than EPI and almost as well as SRS. These results suggest that the unmodified EPI household sampling scheme may be adequate for rapid appraisal of morbidity prevalence or nutritional status of communities, but that it may not be appropriate for surveys which cover a wider range of topics such as health care, or seek to examine the association of health or nutrition with explanatory factors such as education and socioeconomic status. Other factors such as cost and the ability to monitor interviewers' performance should also be taken into account.