Temporal precision of EPSP-spike coupling is an essential pre-requisite to sustain activity during sparse activity states, which have recently been reported to prevail in numerous cortical regions and layers. Most excitatory cells in mammalian brains, however, qualify as integrator or type-I neurons with notoriously imprecise coupling of spikes to transient depolarizing events. Such \\\'bumps\\\' are typical for sparse activity states, and often push the membrane potential to just supra-threshold values. By combining experimental measures relevant for classification of excitability with generic models of spike dynamics, we investigated the precision of EPSP-spike coupling in neocortical pyramidal cells and show that it can be highly imprecise, as expected for type-I cells, but in the majority of cells displays a striking temporal precision. However, precision of EPSP-spike coupling in most cells can be modulated by physiological variations in input resistance. Surprisingly, unlike previously described for other cells, transition between imprecise and precise spiking in neocortical pyramidal cells is not associated with a switch from integrator to resonator, or type-I to type-II, dynamics. We present a new theoretical model that can explain these surprising results within the framework of two-dimensional dynamical systems theory, and argue that the mechanism described here has a very general applicability, providing means to understand temporal precision of EPSP-spike coupling in a wide variety of neurons.