The photodissociations of jet-cooled IBr and Br-2 molecules have been investigated using high resolution ion imaging methods, at excitation energies just above the thresholds for forming, respectively, I(P-2(3/2)o)+Br(P-2(3/2)o) and Br(P-2(3/2)o)+Br-*(P-2(1/2)o) products from parent molecules in their v(')=0 levels. For such molecules, we observe in both cases, that fragments with larger recoil velocities have markedly reduced angular anisotropy, whereas those from photolysis of IBr molecules with v(')=1 show an essentially constant, limiting anisotropy. Given the monochromaticity of the photolysis radiation, increased recoil velocity of fragments resulting from photolysis of v(')=0 molecules can only be derived from increased parent internal (rotational) energy. The measurements thus provide a particularly clear and direct observation of the breakdown of the axial recoil approximation as applied to the photodissociation of a diatomic molecule, and have been modeled, quantitatively, using both quantum and semiclassical methods together with the best available potential energy curves for the relevant excited states of IBr and Br-2.