Several contrasting hypotheses have been formulated about the influence of functional and conformational properties, like stability and avoidance of misfolding, on the evolution of protein globular domains. Selection at functional sites has been suggested to be detrimental to stability or coupled to it. Avoidance of misfolding may be achieved by discarding misfolding-prone sequences or by maintaining a stable native state and thus destabilizing partially or fully unfolded states from which misfolding can take place. We have performed a hierarchical analysis of a large database of point mutations to dissect the relative contributions of function, stability and misfolding in the evolution of natural sequences. We show that at catalytic sites, selection for function overrules selection for stability but find no evidence for an anticorrelation between function and stability. Selection for stability plays a secondary role at binding sites, but is not fully coupled to selection for function. Remarkably, we did not find a selective pressure against misfolding-prone sequences in globular proteins at the level of individual positions. We suggest that such a selection would compromise native-state stability due to a correlation between the stabilities of native and misfolded states. Stabilization of the native state is the most frequent way in which natural proteins avoid misfolding.