Reconstructions of Common-Era sea level are informative of relationships between sea level and natural climate variation, and the uniqueness of modern sea-level rise. Kench et al. recently reconstructed Common-Era sea level in the Maldives, Indian Ocean, using coral microatolls. They reported periods of 150-500 yr when sea level fell and rose at average rates of 2.7-4.3 mm/yr. These periods coincided with intervals of cooling and warming inferred from proxy reconstructions of sea-surface temperature (SST) and radiative forcing (ref. 2, Fig. 2). Kench et al. reasoned that these 0.6-1.4-m centennial-scale sea-level fluctuations were driven by climate, specifically thermal contraction and expansion of seawater. In contrast to previous studies, Kench et al. argued that modern rates and magnitudes of sea-level rise caused by climate change have precedent during the Common Era. We use principles of sea-level physics to argue that pre-industrial radiative forcing and SST changes were insufficient to cause thermosteric sea-level (TSL) trends as large as reported for the Maldives.