NOVELTY - An impure feed gas stream (2) is contacted with a solvent stream (4) to provide a gas stream (6) and solvent effluent bottoms stream (8). Stream (8) is contacted with a recycled vapor fraction (10) of solvent effluent bottoms stream (12) to provide gas stream (14). Stream (12) is flash-separated to provide vapor fraction(s) (16a,16b) and gas-depleted liquid fractions (20a,20b) of stream (12). A purified carbon dioxide product gas stream (22) is recovered from the gas-depleted liquid fraction.    USE - Two-stage gas purification e.g. natural gas purification.    ADVANTAGE - The method improves the recovery and purity of not only methane (and/or other light hydrocarbons in the impure feed gas), but also that of the carbon dioxide contaminant gas. The carbon dioxide product gas has a purity such that it is directly applicable in a number of industrial applications, including enhanced oil recovery.    DETAILED DESCRIPTION - An impure feed gas stream comprising methane and carbon dioxide is contacted with a solvent stream in a counter-current absorber (100) to provide a methane-enriched overhead gas stream and solvent effluent bottoms stream (8) comprising absorbed methane and absorbed carbon dioxide. Stream (8) is contacted with a recycled vapor fraction of solvent effluent bottoms stream (12) in a counter-current stripper (200) to provide methane-enriched overhead gas stream (14) and stream (12). Stream (12) is flash-separated in flash separator(s) (300a,300b,400) to provide vapor fraction(s) of bottoms stream (12) and a gas-depleted liquid fraction of stream (12). A purified carbon dioxide product gas stream is recovered from the gas-depleted liquid fraction of stream (12).    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of the two-stage process for purifying an impure, methane-containing feed gas to provide the recovered, carbon dioxide as a purified product gas.    Impure feed gas stream (2)    Solvent stream (4)    Methane-enriched overhead gas stream (6,14)    Solvent effluent bottoms stream (8,12)    Recycled vapor fraction (10)    Vapor fractions (16a,16b)    Gas-depleted liquid fractions (20a,20b)    Purified carbon dioxide product gas (22)    Counter-current absorber (100)    Counter-current stripper (200)    Flash separators (300a,300b,400)