The number of people to select within selected households has significant consequences for the conduct and output of household surveys. The operational and data quality implications of this choice are carefully considered in many surveys, but the impact on statistical efficiency is not well understood. The usual approach is to select all people in each selected household, where operational and data quality concerns make this feasible. If not, one person is usually selected from each selected household. We find that this strategy is not always justified, and develop intermediate designs between these two extremes. Current practices were developed when household survey field procedures needed to be simple and robust, however more complex designs are now feasible due to the increasing use of computer-assisted interviewing. We develop more flexible designs by optimising survey cost, based on a simple cost model, subject to a required variance for an estimator of population total. The innovation lies in the fact that household sample sizes are small integers, which creates challenges in both design and estimation. The new methods are evaluated empirically using census and health survey data, showing considerable improvement over existing methods in some cases.