An account is given of the description of the low-energy properties of the odd Sn nuclei in terms of number projected one-(1 q.p.) and three-quasiparticle (3 q.p.) states. The shell model space for the neutrons consists of one major shell. A simple Gaussian force is used as an effective interaction. Its strength and the single-particle energies, which are the only parameters, are derived in a consistent way from spectroscopic data on the onequasiparticle states. We find that the spectra can be well interpreted in terms of l q.p. and 3q.p. states. Branching ratios of gamma decay, one-nucleon transfer spectroscopic factors, electric and magnetic moments show generally good agreement with the experimental data. For halflives and mixing ratios, which are most sensitive to details of the 3 q.p. components, the agreement is less, but all have the correct order of magnitude.