Single-crystalline KY 1-x-y-z Gd x Lu y Yb z (WO 4 ) 2 layers are grown onto undoped KY(WO 4 ) 2 substrates by liquid-phase epitaxy. The purpose of co-doping the KY(WO 4 ) 2 layer with suitable fractions of Gd 3? and Lu 3? is to achieve lattice-matched layers that allow us to engineer a high refractive-index contrast between waveguiding layer and substrate for obtaining tight optical mode confinement and simultaneously accommodate a large range of Yb 3? doping concentrations by replacing Lu 3? ions of similar ionic radius for a variety of optical amplifier or laser applications. Crack-free layers, up to a maximum lattice mismatch of *0.08 %, are grown with systematic variations of Y 3? , Gd 3? , Lu 3? , and Yb 3? concentrations, their refractive indices are measured at several wavelengths, and Sellmeier dispersion curves are derived. The influence of co-doping on the spectroscopy of Yb 3? is investigated. As evidenced by the experimental results, the lattice constants, refractive indices, and transition crosssections of Yb 3? in these co-doped layers can be approximated with good accuracy by weighted averages of data from the pure compounds. The obtained information is exploited to fabricate a twofold refractive-index-engineered sample consisting of a highly Yb 3? -doped tapered channel waveguide embedded in a passive planar waveguide, and a cladding-side-pumped channel waveguide laser is demonstrated.