Using magnetoabsorption and electroabsorption techniques, we study excitons with binding energy comparable to the depth of GaAs/AlGaAs quantum wells. In-plane magnetic fields decrease the exciton linewidth considerably. Without magnetic fields, electroabsorption reveals 3D-like exciton behavior. This broadening persists with magnetic fields along the growth direction, but changes to a redshift for in-plane magnetic fields, reminiscent of 2D-like excitons. We discuss how in-plane magnetic fields change the nature of the exciton by inducing a two-body velocity-dependent interaction. © 1996 American Physical Society.