A process for removing light components from an ethylene stream may include providing a dried ethylene stream containing ethylene, ethane, CO, CO2, H2, CH4, and C3+ hydrocarbons. The process may include sending the dried ethylene stream to a stripper to produce an overhead stream containing ethylene, CO, H2 and CH4, and a bottom stream containing ethylene, ethane, CO2, and C3+ hydrocarbons. The gaseous phase on top of the stripper may be condensed in a heat exchanger cooled by a refrigerant stream to get a first gaseous phase and a first liquid phase. The first gaseous phase may be condensed in a heat exchanger cooled by liquid ethane or liquid ethylene to get a second gaseous phase containing ethylene CO, H2 and CH4 and a second liquid phase. The first and second liquid phases may be the reflux of the stripper.