The nuclear level density is one of the main ingredients for the statistical description of the fission process. In this work, we propose to constrain the description of this parameter by using fission reactions induced by protons and light ions on Pb208 at high kinetic energies. The experiment was performed at GSI (Darmstadt), where the combined use of the inverse kinematics technique with an efficient detection setup allowed us to measure the atomic number of the two fission fragments in coincidence. This measurement permitted us to obtain with high precision the partial fission cross sections and the width of the charge distribution as a function of the atomic number of the fissioning system. These data and others previously measured, covering a large range in fissility, are compared to state-of-the-art calculations. The results reveal that total and partial fission cross sections cannot unambiguously constrain the level density at ground-state and saddle-point deformations and additional observables, such as the width of the charge distribution of the final fission fragments, are required.