There is a great interest in the behavior of diatomic molecular solids under extremely high-pressure conditions that lead to pressure-induced metallization, molecular dissociation, and formation of atomic phase. The consensus has been that the phase-transition sequence that happened in both solid bromine and iodine is from a molecular phase (phase I), to an incommensurate phase (phase V), and then to an atomic phase (phase II), with increasing pressure. However, a puzzle remains unresolved for both solids: pressure-induced X and Y bands were observed in the Raman spectra in the molecular phase at low pressures, even before the onset of phase V. Here, we suggest a phase for solid iodine in such a low-pressure range (designated as phase I') in which two different covalent intramolecular bonds coexist, based on first-principles calculations and later corroborated by x-ray diffraction experiments. The pressure dependence of the X and Y bands and other vibrational frequencies measured experimentally can be explained nicely by combining the vibrational modes of phase I and phase I'. These results help improve our understanding on the pressure-induced molecular dissociation and metallization in diatomic solids and may shed some light on the investigation of similar phenomena in solid H(2).