The invention provides a monomode optical fiber and a monomode preform (2) having a mother preform (22) housed in an outer sleeve tube (20). It is characterized in that it also includes an intermediate tube (21) between the mother preform (22) and the outer tube (20), the intermediate tube (21) possessing viscosity at fiber-drawing temperature which is less than the viscosity(ies) at fiber-drawing temperature of the mother preform (22) and of the outer tube (20). The invention also provides a method of manufacturing a monomode optical fiber. The fiber has a core that is better centered and less deformed than in the prior art. An application of the invention lies in making an optical amplifier.