The creation of hyperentangled photons entails the two-photon emission over relatively wide extent in frequency and transverse space; generated photons are thus simultaneously entangled in energy, momentum and polarization. Because the creation process runs in nonlinear domain(s) which is always dispersive and birefringent, the output two-photon state undergoes loss of relative-phase coherence over frequency and space. This offers the vital role of spatial-spectral phase compensation so as to restore partially the state coherence in the two degrees of freedom. Behind compensation, the two-photon state emerges with much better phase flatness allowing collection over wider spatial and spectral ranges. However, as the spatial or spectral modes become further from the central compensated modes, stronger phase variations appears to dominate the scene. This excites two important experimental questions; what is the optimal combination of spatial and spectral filters a) that minimizes the overall phase variations at a given two-photon flux counts? b) that maximizes the two-photon counts at some accepted phase range? Here we address an experimentally convenient approach to determine the best answers of these two questions. The optimization process of the throughput-purity trade-off draws the main guidelines to design hyperentanglement sources whose intrinsic role in several protocols of quantum information and quantum computation.