Process for making a hydrogen-containing synthesis gas (105) from a hydrocarbon feedstock (101), comprising the reforming of said hydrocarbon feedstock and purification of raw synthesis gas, said purification comprising shift conversion of carbon monoxide into carbon dioxide and subsequent absorption of carbon dioxide into an absorbing medium (7a, 14), resulting in a stream of a CO2-rich medium (5), and regeneration of said medium with recovery of CO2 absorbed therein, wherein said raw synthesis gas (102) is produced by the reforming step at a pressure of at least 45 bar, said regeneration of the CO2-loaded medium includes a step of chemical regeneration and the CO2-loaded medium has a temperature of at least 150° C. during said chemical regeneration.