Removing anchored spirals from obstacles is an important step in terminating cardiac arrhythmia. Conventional anti-tachycardia pacing (ATP) has this ability, but only under very restrictive conditions. In a generic model of excitable media, we demonstrate that for unpinning spiral waves from obstacles this profound limitation of ATP can be overcome by far field pacing (FFP). More specifically, an argument is presented for why FFP includes and thus can only extend the capabilities of ATP in the configurations considered. By numerical simulations, we show that in the model there exists a parameter region in which unpinning is possible by FFP but not by ATP. The relevance of this result regarding clinical applications is discussed.