Using spin-polarized neutrons, we propose to determine accurately the T-regimes in which the spin excitation spectrum exhibits marked changes in superconducting YBa2Cu3O6.6. In such a sample, several electronic instabilities occur : (i) an intra-unit-cell magnetic order upon entering the mysterious pseudo-gap phase at T* ~250 K, (ii) an incipient charge density wave state at Tcdw ~ 150 K, (iii) a d-wave SC state at Tc = 62 K. While experimentalists agree on the main features characterizing the renormalization of the spin excitation spectrum upon entering the superconducting state, there is still a large discrepancy among different unpolarized INS studies concerning the exact evolution of the spin excitation spectrum in the normal state. To a large extent, this is due to the difficulty to accurately remove the nuclear background at high temperature. This problem can be overcome by a more extensive use of spin-polarized neutrons.