We report on a detailed investigation of the combined effect of alloying and compression on the structural stability of random bcc and hcp alloys in the Mo-Re system. We use the linear-muffin-tin-orbital Green's-function method within the coherent potential approximation (LMTO-GF-CPA) and the full-potential linear-muffin-tin-orbital (FP-LMTO) method. For pure Mo we find a bcc to hcp transition pressure to take place at 620 GPa (FP-LMTO) or 730 GPa Mbar (LMTO-GF-CPA). The calculated equation of states for Mo68Re32 alloy is in good agreement with the experimental, data, and the calculated bcc-hcp transition pressure is above 400 GPa. This number is much higher than the one anticipated in earlier model calculations. The agreement between the model calculations, ab initio calculations, and the experiment is restored when self-consistent occupation numbers of sp and d electrons are used.