Co-capture of H2S and CO2 by calcium-based sorbents was investigated in a pressurized thermogravimetric reactor with two limestones and one dolomite. Typical test conditions were 850 degrees C and 0.76 MPa. Syngas was used to simulate gasifier conditions. There was complex interaction between the solid product layers and diffusing ions. Careful control of co-capture operating conditions could cause the cyclic performance of limestone sorbents to approach that where no H2S was present. Cyclic operation could lead to higher extents of sulfidation than for H2S alone under comparable conditions. H2S is much less of a problem than SO2 in impeding CO2 capture, even though both reaction irreversibly with lime and limestone under conditions of practical interest.