Loop oscillations have been abundantly reported in recent years. Earlier analytical studies of loop oscillations consider freely propagating waves, allowing for line-tying by a quantization of the wavenumber. Here we consider the rich spectrum of fast MHD modes (both standing and leaky) in coronal loops, allowing for line-tying and performing some comparisons with observational data. We point out that in a straight and homogeneous cylindrical flux tube there should be observational signatures of the excitation of higher order harmonics. Our results indicate that these modes become leaky with the addition of the chromospheric structure at the base of the loop. Leakage can be quite efficient in damping the oscillations for many of these high frequency (compared to fundamental) modes. Appendix A is only available in electronic form at http://www.edpsciences.org