New hybrid Molecular Dynamics-Monte Carlo methods are proposed to increase the efficiency of constant-pressure simulations. Two variations of the isobaric Molecular Dynamics component of the algorithms are considered. In the first, we use the extended-ensemble method of Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)]. In the second, we arrive at a new constant-pressure Monte Carlo technique based on the reversible generalization of the weak-coupling barostat [H. J. C. Berendsen , J. Chem. Phys. 81, 3684 (1984)]. This latter technique turns out to be highly effective in equilibrating and maintaining a target pressure. It is superior to the extended-ensemble method, which in turn is superior to simple volume-rescaling algorithms. The efficiency of the proposed methods is demonstrated by studying two systems. The first is a simple Lennard-Jones fluid. The second is a mixture of polyethylene chains of 200 monomers.