You need to keep even distribution of edges on the cylinder, otherwise you ruin your cylinder shape. So use the original vertical edges of the cylinder as control loop, without adding more or moving them. If you need to edge to more defined you may need more edges on the cylinder.
Napoleon X, you need twice as many polygon spans running down the shaft in order to smooth out that shape properly. So if you have 12 sided cylinder, you really need a 24 sided cylinder to be able to maintain the curvature or else you wind up with lumpy potatoes.