We discuss fiber designs that have been suggested for the reduction of Bragg-grating induced coupling to cladding modes. The discussion is based on a theoretical approach that includes the effect of asymmetry in the W-induced index grating made by UV-side writing. Experimental results from gratings in a depressed-cladding fiber are compared with simulations. The model gives good agreement with the measured transmission spectrum and accounts for the pronounced coupling to asymmetrical cladding modes, even when the grating is written with smallest possible blaze. The asymmetry causing this is accounted for by the unavoidable attenuation of the UV light. It is found for the considered fiber designs that a high numerical-aperture fiber increases the spectral separation between the Bragg resonance and the onset of cladding-mode losses. A depressed-cladding fiber reduces the coupling strength to the lower order cladding modes, and the W-sensitive cladding design reduces the cladding-mode coupling loss. The analysis suggests that the UV-sensitive cladding design is the most effective in reducing the cladding-mode-coupling losses.184255272