  Non-orthogonal bases of projectors on coherent states are introduced to
expand hermitean operators acting on the Hilbert space of a spin s. It is shown
that the expectation values of a hermitean operator A in a family of
(2s+1)(2s+1) spin-coherent states determine the operator unambiguously. In
other words, knowing the Q-symbol of A at (2s+1)(2s+1) points on the unit
sphere is already sufficient in order to recover the operator. This provides a
straightforward method to reconstruct the mixed state of a spin since its
density matrix is explicitly parametrized in terms of expectation values.
Furthermore, a discrete P-symbol emerges naturally which is related to a basis
dual to the original one.
