AbstractWe show that singular integral operators with piecewise continuous coefficients may gain massive spectra when considered in weighted spaces of continuous functions with a prescribed continuity modulus (generalized Hölder spaces Hω (Γ, ρ )), a fact known for example for Lebesgue spaces Lp (Γ, ρ ) in the case of general Muckenhoupt weights ρ or bad‐behaved curves Γ. In the case under consideration the appearance of “lunes” generating massivity of the spectra is due to the presence of a general (non‐equilibrated) continuity modulus ω . These lunes arise when the Boyd‐type indices of the function ω (h ) do not coincide. Thus, the massive spectra may appear in the non‐weighted case and on nice curves, a situation similar to Orlicz spaces. The main problems arising in the investigation are the nature of non‐equilibrated continuity moduli ω and the failure of the density of “nice” functions in Hölder‐type spaces. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)