The hypothesis of self-organised criticality (SOC) predicts that certain open dissipative systems evolve to a critical state where all energy release statistics display power law distributions for event occurrence, size and duration. This has motivated sandpile simulations of magnetospheric energy confinement and release events (avalanches), previous examples of which have taken the limit where energy inflow (fueling) is slow relative to dissipation, and either uniform or random. However the magnetospheric system has both slow and fast periods mixed together in observations, and naturally modulated fueling. We have developed an avalanche model with variable, modulated fueling rate. The power law form for the distribution of energy release events is the least ambiguous current indicator of SOC; we show that this is preserved for the large avalanches in such a system under both constant and varying loading and so such systems are remarkably efficient at eliminating small scale information about their fuelling. ¿ 1999 American Geophysical Union