Crossover valve systems and corresponding methods offer an effective means to overcome large opening pressure force, or provide reasonable gas flow area, or both. In an exemplary embodiment, a crossover valve system for a split-cycle engine having a power cylinder and a crossover passage comprises first and second crossover valves, each valve opening outwardly away from the power cylinder and providing fluid communication between the power cylinder and the crossover passage, with the diameter of the second crossover valve being larger than the diameter of the first crossover valve; and an actuation mechanism operative to open the first crossover valve, then the second crossover valve after a predetermined delay to allow a certain rise in the pressure inside the power cylinder, resulting in much smaller differential pressure forces across the crossover valves, larger flow areas, or both.