Pyramidal neuron (PN) dendrites compartmentalize voltage signals and can generate local spikes, which has led to the proposal that their dendrites act as independent computational subunits within a multilayered processing scheme. However, when a PN is strongly activated, back-propagating action potentials (bAPs) sweeping outward from the soma synchronize dendritic membrane potentials many times per second. How PN dendrites maintain the independence of their voltage-dependent computations, despite these repeated voltage resets, remains unknown. Using a detailed compartmental model of a layer 5 PN, and an improved method for quantifying subunit independence that incorporates a more accurate model of dendritic integration, we first established that the output of each dendrite can be almost perfectly predicted by the intensity and spatial configuration of its own synaptic inputs, and is nearly invariant to the rate of bAP-mediated "cross-talk" from other dendrites over a 100-fold range. Then, through an analysis of conductance, voltage, and current waveforms within the model cell, we identify three biophysical mechanisms that together help make independent dendritic computation possible in a firing neuron, suggesting that a major subtype of neocortical neuron has been optimized for layered, compartmentalized processing under in-vivo-like spiking conditions.