The paper investigates the relationship between risk, capital and efficiency for Islamic and conventional banks using a dataset spanning 14 countries. We use the z-score as a proxy for insolvency risk, cost efficiency is estimated via a stochastic frontier approach and capitalisation is reflected on the equity to assets ratio. An array of bank-specific, macroeconomic and market structure variables are used in a system of three equations, estimated using the seemingly unrelated regression (SUR) technique. We find that the capitalisation response to increases in insolvency risk is more pronounced for Islamic banks but has an approximately five-times smaller effect on risk mitigation compared to conventional banks. Higher cost efficiency is related to lower risk for conventional banks, but the opposite is true for Islamic banks. The link between cost efficiency and capitalisation attests to a substitutional effect for the case of conventional banks, but a complementary effect for Islamic banks. Our findings give new insights on the use of efficiency to gauge capital requirements for financial institutions and are particularly relevant for regulators and policy makers in countries where both bank types operate.