Recent studies have shown that the observed global warming trend over recent decades provides efficient constraints not only for future global mean temperature increases (ΔTgm) across Earth system models but also for changes in several climate variables that include significant ΔTgm–related uncertainty. However, ΔTgm–related emergent constraints (ECs) cannot reduce the uncertainty unrelated to ΔTgm. Here, to overcome this limitation, we develop an EC method and apply it to future changes in the annual maximum daily precipitation in order to reduce uncertainty therein. An EC for precipitation sensitivity based on historical extreme precipitation biases is combined with the constrained ΔTgm. This combined EC decreases the variance of the global mean precipitation by 42%, an improvement from only using temperature (resulting in 26% reduction), and the variance of regional precipitation by ≥ 30% in 24% of the globe (whereas ≥ 30% reduction is only seen in 2% of the globe with the temperature-related EC).