In vivo recordings have shown that the discharge of cortical neurons is often highly variable and can have statistics similar to a Poisson process with a coefficient of variation around unity. To investigate the determinants of this high variability, we analyzed the spontaneous discharge of Hodgkin-Huxley type models of cortical neurons, in which in vivo-like synaptic background activity was modeled by random release events at excitatory and inhibitory synapses. By using compartmental models with active dendrites, or single compartment models with fluctuating conductances and fluctuating currents, we found that a high discharge variability was always paralleled with a high-conductance state, while some active and passive cellular properties had only a minor impact. Furthermore, a balance between excitation and inhibition was not a necessary condition for high discharge variability. We conclude that the fluctuating high-conductance state caused by the ongoing activity in the cortical network in vivo may be viewed as a natural determinant of the highly variable discharges of these neurons.