We consider the combined effects of active dendrites and structural plasticity on the storage capacity of neural tissue. We compare capacity for two different modes of dendritic integration: (1) linear, where synaptic inputs are summed across the entire dendritic arbor, and (2) nonlinear, where each dendritic compartment functions as a separately thresholded neuron-like summing unit. We calculate much larger storage capacities for cells with nonlinear subunits and show that this capacity is accessible to a structural learning rule that combines random synapse formation with activity-dependent stabilization/elimination. In a departure from the common view that memories are encoded in the overall connection strengths between neurons, our results suggest that long-term information storage in neural tissue could reside primarily in the selective addressing of synaptic contacts onto dendritic subunits.