A method and a component for despreading a multi-code signal that has been generated using two or more spreading codes with different spreading factors are described. The method comprises subjecting the signal to a first despreading step (40) that includes a first Fast Hadamard Transform (FHT) to jointly despread the spreading codes. During the first despreading step one or more spreading codes are despread only partially. The signal or signal portion including one or more partially despread spreading codes are then subjected to one or more further despreading steps (42).