We show that coupling the SU(2)-valued Skyrme field to the rho-meson solves the long-standing issue of (in)compressibility in the solitonic Skyrme model. Even by including only one rho pi interaction term, motivated by a holographic-like reduction of Yang-Mills action by Sutcliffe, reduces the compression modulus from K0 similar or equal to 1080 MeV, in the massive Skyrme model, to K0 similar or equal to 351 MeV.