The formation of amyloid fibrils in Alzheimer's disease and other neurodegenerative disorders is limited by a slow nucleation step due to the entropic cost to initiate the ordered cross-β structure. While the barrier can be lowered if the molecules maintain conformational disorder, poorly ordered clusters provide a poor binding surface for new molecules. To understand these opposing factors, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with β-sheet and non-β states. We find that the optimal degree of order in a nucleus depends on protein concentration. Low concentration systems require more ordered nuclei to capture infrequent monomer attachments. The nucleation phase transitions to the elongation phase when the β-sheet core becomes large enough to overcome the initiation cost, at which point further ordering becomes favorable and the nascent fibril efficiently captures new molecules.