In fragile states and areas beset by insecurity and conflict, the time available for a face-to-face interview is typically limited. That prevents administering the lengthy household consumption expenditure surveys used for measuring poverty. This paper presents a new approach to obtain unbiased estimates of poverty when the time to conduct interviews is a binding constraint. The finite list of consumption recall items is partitioned selectively into a core module and algorithmically into nonoverlapping optional modules. Each household is systematically assigned the core module and randomly assigned one of the optional modules. Multiple imputation techniques are then used to estimate total household consumption. Based on ex post simulations, the approach is demonstrated to yield reliable estimates of per capita consumption and poverty using data from a regular household budget survey collected in Hargeisa, Somaliland. The approach is then applied to a survey conducted in Mogadishu where interview time could not exceed 60 minutes.