In the context of heteroclinic networks the term ’switching’ refers to a particular form of complex dynamics near the network: Trajectories follow any possible sequence of connections that can be prescribed given the network architecture. We consider simple heteroclinic networks in Rn and give sufficient conditions for the absence of a weak form of switching (i.e. along a connection that is common to two cycles), generalizing a similar result in the work of M. Aguiar (Physica D 240, 1474-1488, 2011). In particular, we illustrate that these conditions are natural for networks made up of cycles of types A and Z, and look at two examples of networks in R5 that show what kind of dynamics may occur if they are broken.