Partial-order reduction (POR) is a well-established technique to combat the problem of state-space explosion. We propose POR techniques that are sound for parity games, a well-established formalism for solving a variety of decision problems. As a consequence, we obtain the first POR method that is sound for model checking for the full modal mu-calculus. Our technique is applied to, and implemented for the fixed point logic called parameterised Boolean equation systems, which provides a high-level representation of parity games. Experiments indicate that substantial reductions can be achieved.