The invention concerns a method for controlling the fuel supply to an internal combustion engine at start-up. The fuel supply system can be set in at least two start modes, a lean mode and a rich mode, and the selection of mode is based on an evaluation of a previous start attempt or successful run. The invention also concerns a carburetor (10) having a fuel supply system including a main fuel path (13) with an actively controlled fuel valve (26) and an idling fuel path (14) branching off from the main fuel path (13) downstream of the valve (26). The fuel supply system further includes a start fuel line (23, 423) starting upstream (FIG. 1) or downstream (FIG. 4) of the fuel valve (26) and ending in at least one start fuel outlet near and downstream of a choke valve.