For any positive integer r, denote by Pr the set of all integers 2 Z having at most r prime divisors. We show CPr (T), the space of all continuous functions on the circle T whose Fourier spectrum lies in Pr, contains a complemented copy of '1. In particular, CPr (T) is not isomorphic to C(T), nor to the disc algebra A(D). A similar result holds in the L1 setting.