Two concretes—with Ca/Si ratios of 0.28 and 1.75 fabricated by cementing a fine‐limestone aggregate with a mixture of lime, diatomaceous earth, and water—were compared with ones made with pure lime and a hydraulic lime product, containing ∼11 wt% naturally occurring reactive silica. When the Ca/Si ratio in the cementing phase was 0.28, compressive strengths of ∼6.5 MPa after 30 days and ∼7 MPa after 180 days were achieved by curing the samples in closed containers or in 100% relative humidity. When allowed to dry, however, these samples lost roughly half their compressive strength in 7 days. Increasing the Ca/Si ratio to 1.75 solved the drying problems. The resulting compressive strengths, however, after 180 days, were reduced to 5 MPa. Characterization of the various cementing phases formed in the different samples by X‐ray diffraction, Fourier transform infrared spectroscopy, and thermogravimetric analysis showed the formation of two, somewhat competing, cementing reactions: C–S–H gel formation which results in early strength gains, and the recarbonation of portlandite, which results in longer term strength enhancements.