The dendritic spines of many central neurons are generally thought to modulate the ability of individual synaptic conductances to depolarize the dendritic shaft. A compartmental analysis using typical spine dimensions shows that spine neck resistances are probably far too low to support such a function, because low conductance synapses act as time-varying current sources. However, the collective presence of all spines on a dendrite significantly modifies the electrical properties of the branch in ways which have previously been overlooked. In particular, they lower its input impedance and length constant, reducing the amplitude of the unitary excitatory postsynaptic potential as well as the strength of spatial summation. This enables a dendrite to integrate large numbers of synaptic inputs while occupying minimal volume. In this way, dendritic spines are analogous to axonal myelin, which also alters transcellular impedance in order to maximize neurite function and minimize volume. Unlike membrane resistance changes, spines have little effect on the membrane time-constant so they maintain a long window for temporal summation. Though spine shape and neck resistance do not significantly affect dendritic potentials, spine area does. Therefore, while changes in spine morphology probably do not directly potentiate the strength of individual synapses, changes in spine density can regulate the synaptic excitability of an entire dendrite. The shortened length-constant of the spiny dendrite requires excitable membranes to be located in distal dendrites. These, in turn, eliminate many of the electrotonic nonlinearities associated with summation in long, thin processes, and make all distal synapses equipotent. The short length-constant also enhances the sensitivity of dendritic spikes to local impedance changes while decreasing the sensitivity to distant impedance changes. This would enable a neuron to effectively use inhibitory synapses or branch points to regulate propagation through its spiny dendritic tree. A model neuron is developed in which dendritic spines, excitable membranes, and dendritic branching combine to form a two-stage filter, which serves as a synaptic input coincidence detector with adjustable gain. Gain is regulated by potassium conductances which modulate branch point safety factor. The model is consistent with the notion of functional independence of distal dendrites and demonstrates that certain aspects of dendritic spiking which have previously been thought to require membrane hot-spots can also result from geometrical properties. It is suggested that the activation of spiny neurons may depend as much on the density as on the number of active synapses, and that spiny neurons may tend to have discrete output states whereas nonspiny neurons may be more continuous.