Almost 90 years ago, Lillie reported that rapid saltatory conduction arose in an iron wire model of nerve impulse propagation when he covered the wire with insulating sections of glass tubing equivalent to myelinated internodes. This led to his suggestion of a similar mechanism explaining rapid conduction in myelinated nerve. In both their evolution and their development, myelinating axons must make a similar transition between continuous and saltatory conduction. Achieving a smooth transition is a potential challenge that we examined in computer models simulating a segmented insulating sheath surrounding an axon having Hodgkin-Huxley squid parameters. With a wide gap under the sheath, conduction was continuous. As the gap was reduced, conduction initially slowed, owing to the increased extra-axonal resistance, then increased (the "rise") up to several times that of the unmyelinated fiber, as saltatory conduction set in. The conduction velocity slowdown was little affected by the number of myelin layers or modest changes in the size of the "node," but strongly affected by the size of the "internode" and axon diameter. The steepness of the rise of rapid conduction was greatly affected by the number of myelin layers and axon diameter, variably affected by internode length and little affected by node length. The transition to saltatory conduction occurred at surprisingly wide gaps and the improvement in conduction speed persisted to surprisingly small gaps. The study demonstrates that the specialized paranodal seals between myelin and axon, and indeed even the clustering of sodium channels at the nodes, are not necessary for saltatory conduction.