To study the mechanisms of bursting, we have constructed a conductance-based, one-compartment model of CA1 pyramidal neurons. In this neuron model, reduced [Ca2+]o is simulated by negatively shifting the activation curve of the persistent Na+ current (INaP), as indicated by recent experimental results. The neuron model accounts, with different parameter sets, for the diversity of firing patterns observed experimentally in both zero and normal [Ca2+]o. Increasing INaP in the neuron model induces bursting and increases the number of spikes within a burst, but is neither necessary nor sufficient for bursting. We show, using fast-slow analysis and bifurcation theory, that the M-type K+ current (IM) allows bursting by shifting neuronal behavior between a silent and a tonically-active state, provided the kinetics of the spike generating currents are sufficiently, though not extremely, fast. We suggest that bursting in CA1 pyramidal cells can be explained by a single compartment *square bursting* mechanism with one slow variable, the activation of IM. See paper for more and details.