Predicting function from sequence is an important goal in current biological research, and although, broad functional assignment is possible when a protein is assigned to a family, predicting functional specificity with accuracy is not straightforward. If function is provided by key structural properties and the relevant properties can be computed using the sequence as the starting point, it should in principle be possible to predict function in detail. The truncated hemoglobin family presents an interesting benchmark study due to their ubiquity, sequence diversity in the context of a conserved fold and the number of characterized members. Their functions are tightly related to O2 affinity and reactivity, as determined by the association and dissociation rate constants, both of which can be predicted and analyzed using in-silico based tools. In the present work we have applied a strategy, which combines homology modeling with molecular based energy calculations, to predict and analyze function of all known truncated hemoglobins in an evolutionary context. Our results show that truncated hemoglobins present conserved family features, but that its structure is flexible enough to allow the switch from high to low affinity in a few evolutionary steps. Most proteins display moderate to high oxygen affinities and multiple ligand migration paths, which, besides some minor trends, show heterogeneous distributions throughout the phylogenetic tree, again suggesting fast functional adaptation. Our data not only deepens our comprehension of the structural basis governing ligand affinity, but they also highlight some interesting functional evolutionary trends. 