An improved tapered fiber bundle (TFB), or assembly including a TFB, mitigates undesirable reflections from optical discontinuities at the input ends of the multimode fibers of the TFB by suppressing the coupling of signal light into modes that can produce undesired reflections. Means are provided for managing the mode field of injected signal light so that it remains substantially confined to the core of the central TFB fiber until it is past the region where it can interact with the multimode fibers of the TFB.