The costs of removing red tape include a lower chance of detecting recession‐generating flaws in the financial system. What we call independent dimensions of regulation (IDRs) operate more or less independently from other groupings. If an IDR's optimality is unknown, it may be risky to remove. Uncertainty thus implies that (some) red tape – a small amount of overregulation – is justified, in contrast to the Brainard principle that uncertainty dictates less policy activism. The long‐run Gross Domestic Product (GDP) benefit of a 1 per cent improvement in financial services productivity is 0.06 per cent in our computable general equilibrium model. These relatively modest gains reinforce our conclusion.