Populations of cortical neurons can respond to changes in their common input within about a millisecond. However, that response speed has a pronounced dependence on the temporal statistics of the neuron's input (Tchumatchenko etal.2011, Merino etal. 2021, Revah etal. 2024). Slowly fluctuating inputs allow for much more rapid responses. In the dynamic gain function of the individual neuron, this corresponds to a wider bandwidth under slower input correlations. Fourcaud etal. (2003) demonstrated that a wide bandwidth requires a strong voltage dependence of the action potential initiating currents. The observed voltage dependence of neuronal sodium channels is too low to explain the observed fast response. Furthermore, simple biophysically inspired models (eg. exponential integrate and fire - EIF) show a weak dependence on input correlations at most provided the operating points are chosen appropriately for all correlation times (Zhang etal. 2024).Here we study the response properties of simple, EIF-derived models. We show that the fast response can be achieved with realistic ion channel properties if subthreshold potassium channel activation is taken into account. This also introduces the experimentally observed broadening of the dynamic gain bandwidth as the input correlation time increases. in addition, experimental evidence for the critical influence of potassium channels on the response speed is presented.