We apply the Ljusternik-{hacek S}nirelman theory, a derivative of Morse theory, to the Skyrmion-Skyrmion potential in the two-flavor Skyrme model to look for the existence of new, static, classical solutions in the sector with baryon number two. Concomitantly, we present a systematic method for obtaining an expansion of this potential, in inverse powers of the separation, when the separation is large.