A numerical study is presented of the phenomenology of ignition, and initiation of combustion waves, in a model representing a spherical power source embedded in a concentric spherical volume of combustible material of relatively low exothermicity. For simplicity, one-step chemistry is assumed, and diffusion of oxygen or gaseous products is neglected. The results show unexpected behaviour for small-sized power sources, in which, over a range of source radii, there are two distinct critical values for the power, with an apparently "safe" region occupying some of the range between them. Possible safety implications for chemical plant operation are discussed