Capsules are fundamental informative units that are introduced into capsule networks to manipulate the hierarchical presentation of patterns. The part-hole relationship of an entity is learned through capsule layers, using a routing-by-agreement mechanism that is approximated by a voting procedure. Nevertheless, existing routing methods are computationally inefficient. We address this issue by proposing a novel routing mechanism, namely “shortcut routing”, that directly learns to activate global capsules from local capsules. In our method, the number of operations in the routing procedure is reduced by omitting the capsules in intermediate layers, resulting in lighter routing. To further address the computational problem, we investigate an attention-based approach, and propose fuzzy coefficients, which have been found to be efficient than mixture coefficients from EM routing. Our method achieves on-par classification results on the Mnist (99.52%), smallnorb (93.91%), and affNist (89.02%) datasets. Compared to EM routing, our fuzzy-based and attention-based routing methods attain reductions of 1.42 and 2.5 in terms of the number of calculations.