  The capability to tune the strength of the elastic interparticle interaction
is crucial for many experiments with ultracold gases. Magnetic Feshbach
resonances are a tool widely used for this purpose, but future experiments
would benefit from additional flexibility such as spatial modulation of the
interaction strength on short length scales. Optical Feshbach resonances offer
this possibility in principle, but suffer from fast particle loss due to
light-induced inelastic collisions. Here we show that light near-resonant with
a molecular bound-to-bound transition can be used to shift the magnetic field
at which a magnetic Feshbach resonance occurs. This makes it possible to tune
the interaction strength with laser light and at the same time induce
considerably less loss than an optical Feshbach resonance would do.
