We apply the optimal fingerprint detection algorithm to three independent diagnostics of the recent climate record and derive joint probability density distributions for three uncertain properties of the climate system. The three properties are climate sensitivity, the rate of heat uptake by the deep ocean, and the strength of the net aerosol forcing. Knowing the probability distribution for these properties is essential for quantifying uncertainty in projections of climate change. We briefly describe each diagnostic and indicate its role in constraining these properties. Based on the marginal probability distributions, the 5 to 95% confidence intervals are 1.4 to 7.7K for climate sensitivity and 0.30 to 0.95 W/m² for the net aerosol forcing using uniform priors; and 1.3 to 4.2K and 0.26 to 0.88 W/m² using an expert prior for climate sensitivity. The oceanic heat uptake is not so well constrained. The uncertainty in the net aerosol forcing in either case is much less than the uncertainty range usually quoted for the indirect aerosol forcing alone.