Rising concentrations of atmospheric CO2 are changing the carbonate chemistry of the oceans, a process known as ocean acidification (OA). Absorption of this CO2 by the surface oceans is increasing the amount of total dissolved inorganic carbon (DIC) and bicarbonate ion (HCO3) available for marine calcification yet is simultaneously lowering the seawater pH and carbonate ion concentration ([CO3]), and thus the saturation state of seawater with respect to aragonite. We investigated the relative importance of [HCO3] versus [CO3] for early calcification by new recruits (primary polyps settled from zooxanthellate larvae) of two tropical coral species, Favia fragum and Porites astreoides. The polyps were reared over a range of Oar values, which were manipulated by both acid-addition at constant pCO2 (decreased total [HCO3] and [CO3]) and by pCO2 elevation at constant alkalinity (increased [HCO3], decreased [CO3]). Calcification after 2 weeks was quantified by weighing the complete skeleton (corallite) accreted by each polyp over the course of the experiment. Both species exhibited the same negative response to decreasing [CO3] whether Oar was lowered by acid-addition or by pCO2 elevation--calcification did not follow total DIC or [HCO3]. Nevertheless, the calcification response to decreasing [CO3] was nonlinear. A statistically significant decrease in calcification was only detected between Omega aragonite = <2.5 and Omega aragonite = 1.1-1.5, where calcification of new recruits was reduced by 22-37% per 1.0 decrease in Omega aragonite. Our results differ from many previous studies that report a linear coral calcification response to OA, and from those showing that calcification increases with increasing [HCO3]. Clearly, the coral calcification response to OA is variable and complex. A deeper understanding of the biomineralization mechanisms and environmental conditions underlying these variable responses is needed to support informed predictions about future OA impacts on corals and coral reefs.