Research with humans and primates shows that the developmental course of the brain involves synaptic overgrowth followed by marked selective pruning. Previous explanations have suggested that this intriguing, seemingly wasteful phenomenon is utilized to remove “erroneous” synapses. We prove that this interpretation is wrong if synapses are Hebbian. Under limited metabolic energy resources restricting the amount and strength of synapses, we show that memory performance is maximized if synapses are first overgrown and then pruned following optimal “minimal-value” deletion. This optimal strategy leads to interesting insights concerning childhood amnesia.