Biological solutions for adhesive functions have inspired many scientific developments worldwide. Artificial dry adhesives based on fibrillar surfaces patterns are now available that mimic the multiple attachment and detachment of gecko toes. While such structures have shown satisfactory performance against flat counter surfaces under ideal conditions, i.e. with ideal relative orientation of two surfaces, such circumstances cannot always be guaranteed. Our new developments are aiming at fibrillar adhesives for surfaces with finite roughness: we have shown that, with judicious design of the surface patterns, also rough surfaces are susceptible to a fibrillar size effect and can exhibit useful gripping performance. In addition, with a new composite design, the interfacial stress distributions and the detachment mechanisms can be controlled, making the adhesive performance less sensitive to surface roughness. These developments, which are complemented by numerical simulations, have the potential of greatly enhancing the applicability of bioinspired adhesive surfaces in non-ideal situations.