Crystallization rate experiments performed on the uniform alkanes C//2//4//6H//4//9//4 and C//1//9//8H//3//9//8, by both differential scanning calorimetry and in situ X-ray diffraction (using a synchrotron source), have revealed that these rates, including both primary nucleation and growth, pass through a minimum with increasing supercooling. The first (expected) increase and subsequent (unsuspected) decrease correspond to extended-chain (E) crystallization, the renewed increase beyond the minimum corresponding to chain-folded crystallization with the fold period l being smaller than L but larger than L/2, where L is the extended chain length. The observed effects, which have come to light owing to the availability of ultra-long and uniform n-alkanes, help to provide new insight into the primary stages of chain-folded crystallization, with many potential consequences, some of which are discussed.