In adaptive importance sampling and other contexts, we haveK> 1 unbiased and uncorrelated estimates μ^kof a common quantity μ. The optimal unbiased linear combination weights them inversely to their variances, but those weights are unknown and hard to estimate. A simple deterministic square root rule based on a working model that Var(μ^k) ∝k−1/2gives an unbiased estimate of μ that is nearly optimal under a wide range of alternative variance patterns. We show that if Var(μ^k)∝k−yfor an unknown rate parametery∈[0,1], then the square root rule yields the optimal variance rate with a constant that is too large by at most 9/8 for any 0 ⩽y⩽ 1 and any numberKof estimates. Numerical work shows that rule is similarly robust to some other patterns with mildly decreasing variance askincreases.