Gas-driven filter pressing is the process of melt expulsion from a volatile-saturated crystal mush, induced by the buildup and subsequent release of gas pressure. Filter pressing is inferred to play a major role in magma fractionation at shallow depths (<10 km) by moving melt and gas relative to the solid, crystalline framework. However, the magmatic conditions at which this process operates remain poorly constrained. We present novel experimental data that illustrate how the crystal content of the mush affects the ability of gas-driven filter pressing to segregate melt. Hydrous haplogranite (2.1 wt% water in the melt) and dacite (4.2 wt% water in the melt) crystal mushes, with a wide range of crystallinities (34-80 vol% crystals), were investigated using in-situ, high-temperature (500-800 degrees C) synchrotron X-ray tomographic microscopy with high spatial (3 mm/pixel) and temporal resolution (similar to 8 s per three-dimensional data set). Our experimental results show that gas-driven filter pressing operates only below the maximum packing of bubbles and crystals (similar to 74 vol%). Above this threshold, the mush tends to fracture and gas escapes via fractures. Therefore, the efficiency of gas-driven filter pressing is promoted close to the percolation threshold and in situations where a mush inflates slowly relative to build-up of pressure and expulsion of melt. Such observations offer a likely explanation for the production of eruptible, crystal-poor magmas within Earth's crust.