Homeostatic synaptic plasticity (HSP) has been suggested to act as a negative feedback mechanism responsible for globally and uniformly scaling (up or down) the strength of all synapses in the neuron, in compensation for chronically aberrant (too low or too high) levels of activity. Such global scaling preserves the relative strengths of synapses and thus keeps 'Hebbian-like' memory traces (long-term potentiations, LTP, or depressions, LTD). However, new experimental findings demonstrate that HSP can operate locally, controlling each synapse individually. Seemingly, this finding implies that HSP can abolish any modification of synaptic strength (erase LTP/LTD). We propose that dendrites offer an inherent solution to this 'paradox' and that in fact local HSP might confer upon the neuron several surprising benefits, which are demonstrated using computer simulations.