Experimental studies suggest that the fracture toughness of rocks increases with the confining pressure. Among many methods to quantify this dependency, a so-called burst experiment (Abou-Sayed, 1978) may be the most widely applied in practice. Its thick wall cylinder geometry leads to a stress state resembling the subsurface condition of a pressurized wellbore with bi-wing fractures. The fracture toughness of a sample, under a given confinement pressure, can be recovered from the critical pressure upon which the bi-wing cracks propagate. Traditionally, this critical pressure is thought to correspond to a sudden drop in injection pressure. However, as the standard configuration was deliberately designed to obtain stable fracture growth at the onset, propagation can take place well before this drop in pressure, and one may overestimate the fracture toughness from measured pressures. Here, we study crack stability in the burst experiment and propose modifications to the experimental design which promotes unstable fracture growth and makes the critical pressure less ambiguous to interpret. We found that experiments with the original, stable design can lead to inconsistent measurement of fracture toughness under confining pressure, while results from unstable configurations are more consistent. Our claim on the stability was also supported by the recorded acoustic emissions from both stable and unstable experiments.