More with less: Bethel allocation and precision-preserving sample size reduction via hierarchical Bayes modelling*

National statistical offices face an intensifying dilemma: rising demand for domain-level estimates under fixed or shrinking budgets. This paper presents a practical two-stage strategy for minimising survey sample size while preserving pre-defined precision targets for all target variables across all geographic domains simultaneously. Stage 1 applies Bethel allocation, which finds the globally minimum sample satisfying all coefficient-of-variation (CV) constraints at once. Stage 2 asks whether this Bethel sample can be reduced further via Hierarchical Bayes (HB) small area modelling; a nested sub-sampling algorithm with four eligibility gates identifies the largest achievable reduction. Applied to a synthetic labour-force population ( N = 1,000,000 ; H = 100 strata; D = 10 domains), the strategy reduces the required sample from 91,308 to 18,262 — an 80% reduction — while meeting all national and domain CV targets. A Monte Carlo study ( B = 1,000 ) confirms that CV targets are passed in more than 95% of replications for all three target variables, and credible-interval coverage is close to the nominal 95%. Four sensitivity scenarios varying auxiliary-variable strength, domain heterogeneity, and event rarity confirm that HB achieves an 85% reduction in each case, with the Bethel baseline scaling appropriately to the difficulty of each setting. The principal trade-off is a shift from design-based to model-based inference, whose risks and mitigants are discussed explicitly.