The evolution of a character is better appreciated if examples of convergent emergence of the same character are available for comparison. Three instances are known among invertebrates of the evolution of axonal sheaths possessing the functional properties and many of the structural properties of vertebrate myelin. Comparison of these invertebrate myelins raises the question of what structural features must a sheath possess in order to produce the two principal functional characteristics of impulse speed enhancement and energy savings. This essay reviews the features recognized by early workers as pertaining to myelin in vertebrate and invertebrate alike: osmiophilia, negative birefringence and saltatory conduction. It then examines common features revealed by the advent of electron microscopy: multiplicity of lipid membranes, condensation of those membranes, specialized marginal seals, and nodes. Next it examines the robustness of these features as essential components of a speed-enhancing sheath. Features that are not entirely essential for speed enhancement include membrane compaction, spiral wrapping of layers, glial cell involvement, non-active axonal membrane, and even nodes and perinodal sealing. This permissiveness is discussed in relation to the possible evolutionary origin of myelin.