It is known that variational perturbation theory for fluids with both upper and lower bounds may provide a more accurate estimate of the free energy for dense model fluid. This does not apply in general to the widely used hard-sphere perturbation theory because standard method produces a trivial lower bound of -infinity. In this article, we propose a simple solution and demonstrate the method for the repulsive soft sphere model of r(-n) with n=4, 6, 9, 12, near freezing. The upper and lower bounds accurately bracket the free energy from computer simulations. The arithmetic means of the bounds agrees with the simulations within 0.1 k(B)T.