A method of making a multi-mode optical fiber that includes: depositing a porous germania-doped silica soot to form a germania-doped porous soot preform; depositing a porous silica layer over the porous soot preform; doping the porous soot preform and the porous silica layer with a fluorine dopant to form a co-doped soot preform having a core region and a fluorine-doped trench region; consolidating the co-doped soot preform to form a sintered glass, co-doped core preform having a refractive index alpha profile between 1.9 and 2.2 measured at 850 nm; depositing a cladding comprising silica over the sintered glass, co-doped preform to form a multi-mode optical fiber preform; drawing the optical fiber preform into a multi-mode optical fiber. Further, the step of doping the germania-doped soot preform and the porous silica layer is conducted according to a doping parameter (Φ) that is set between 20 and 300, and given by: Φ = 1 × 10 14 ⁢ R prc 2 ⁢ exp ⁡ ( - E / RT dop ) ⁢ T dop 1 / 2 x 3 / 4 .