Presolar grains from oxygen-neon novae can be identified using their sulphur isotopic ratios. However, these ratios depend on detailed knowledge of the sulphur destruction reactions: 33S(p,γ)34Cl and 34S(p,γ)35Cl. We performed an experiment using the high-resolution TUNL Enge split-pole spectrograph to identify states in 35Cl, which are important for the latter of these two reactions. We were also able to constrain the spins and parities of those states, improving our understanding of the reaction cross section. We found that previous studies did not fully account for the uncertainties in the cross section and prove recommendations for future study