Methods of forming a bandwidth-tuned optical fiber for short-length data transmission systems include establishing a relationship between a change Δτ in a modal delay τ, a change ΔT in a draw tension T and a change Δλ in a BM wavelength λ of light in a BM wavelength range from 840 nm and 1100 nm for a test optical fiber drawn from a preform and that supports BM operation at the BM wavelength. The methods also include drawing from either the preform or a closely related preform the bandwidth-tuned optical fiber by setting the draw tension based on the established relationships of the aforementioned parameters so that the bandwidth-tuned optical fiber has a target bandwidth greater than 2 GHz·km at a target wavelength within the BM wavelength range.