Ocean alkalinity enhancement (OAE) is a method that can remove carbon dioxide (CO₂) from the atmosphere and counteract ocean acidification through the dissolution of alkaline minerals. Currently, critical knowledge gaps exist regarding the dissolution of different minerals suitable for OAE in natural seawater. Of particular importance is to understand how much alkaline mineral can be dissolved before secondary precipitation of calcium carbonate (CaCO₃) occurs, since secondary CaCO₃ precipitation reduces the atmospheric CO₂ uptake potential of OAE. Using two types of mineral proposed for OAE, quick lime (CaO) and hydrated lime (Ca(OH)₂), we show that both (<63 µm of diameter) dissolved in seawater within a few hours. No CaCO₃ precipitation occurred at a saturation state (Ω_A) of ∼5, but CaCO₃ precipitation in the form of aragonite occurred above an Ω_A value of 7. This limit is lower than expected for typical pseudo-homogeneous precipitation, i.e. in the presence of colloids and organic matter. Secondary precipitation at low Ω_A (∼ 7) was the result of heterogeneous precipitation onto mineral surfaces, most likely onto the added CaO and Ca(OH)₂ particles. Most importantly, runaway CaCO₃ precipitation was observed, a condition where significantly more total alkalinity (TA) was removed than initially added. Such runaway precipitation could reduce the OAE CO₂ uptake efficiency from ∼ 0.8 mol of CO₂ per mole of added TA down to 0.1 mol of CO₂ per mole of TA. Runaway precipitation appears to be avoidable by dilution below the critical Ω_A threshold of 5, ideally within hours of the mineral additions to minimise initial CaCO₃ precipitation. Finally, OAE simulations suggest that for the same Ω_A threshold, the amount of TA that can be added to seawater would be more than 3 times higher at 5 ^∘C than at 30 ^∘C. The maximum TA addition could also be increased by equilibrating the seawater to atmospheric CO₂ levels (i.e. to a pCO₂ of ∼ 416 µatm) during addition. This would allow for more TA to be added in seawater without inducing CaCO₃ precipitation, using OAE at its CO₂ removal potential.