Encumbered heme models have been designed over the years to enforce the Fe-C-O unit to adopt a bent geometry as reported earlier in myoglobin and to examine the consequences upon the reactivity. This work deals with "hybrid" heme models in which a variable amount of distal steric hindrance is provided by a chain which is rigidly maintained in a central position above an iron(II) 5, 10, 15, 20-tetraphenylporphyrin (TPP) macrocycle by the presence of two lateral pivalamido pickets. We have investigated the structure-reactivity relationship in the binding of O-2 and CO with these models by determining the X-ray structures of two CO derivatives and the ligand rebinding kinetics using laser flash photolysis. Upon increasing the steric hindrance, CO affinities are decreased by 2-3 orders of magnitude whereas oxygen affinities are only reduced by a factor of 1.4-3.4, indicating a strong steric discrimination against CO. Using linear free energy relationships to compare all encumbered TPP derivatives for which kinetic data have been reported, we find that a total of six compounds reasonably mimic the reactivity of hemoproteins. The crystal structures of hybrid models as well as other available data indicate that the main mechanisms by which steric interaction with CO is released in encumbered TPP derivatives involve a ruffling distortion of the porphyrin ring and an expansion of the distal cavity instead of the expected bending of the Fe-C-O unit. Many recent experimental and theoretical results suggest that the bent angle of Fe-C-O in myoglobin has been largely overestimated. In fact, several mechanisms may be at work simultaneously to release the steric constraints both in heme models and in hemoproteins, depending on the available degrees of freedom. Although modeling the energetic aspects of hemoprotein reactivity does not imply that structural aspects are also well reproduced, the present results provide additional arguments to reconsider the relative contributions of Fe-C-O and porphyrin distortions for modulating the reactivity in oxygen-carrying hemoproteins.