Based on the Hartree-Fock approximation, we perform a detailed calculation of the cohesive energies of the round bubble phase, stripe phase, and possible intermediate states which may appear in the partially-filled high Landau levels in a two-dimensional electron system. Our computation shows that there is a first-order phase transition from bubbles to stripes at the filling factor of the uppermost Landau level ν*~0.35. However, the almost complete independence of the cohesive energy from the bubble's shape near the phase transition point indicates that the real ground state may be very fragile before the critical filling factor.