Two key hypotheses about the structural basis of long-term potentiation (LTP) are evaluated in light of new findings from immature rat hippocampal slices. First, it is shown why dendritic spines do not split during LTP. Instead a small number of spine-like dendritic protrusions may emerge to enhance connectivity with potentiated axons. These ‘same dendrite multiple synapse boutons’ provide less than a 3% increase in connectivity and do not account for all of LTP or memory, as they do not accumulate during maturation. Second, polyribosomes in dendritic spines served to identify which of the existing synapses enlarged to sustain more than a 30% increase in synaptic strength. Thus, both enhanced connectivity and enlarged synapses result during LTP, with synapse enlargement being the greater effect.