A three dimensional continuous space Monte Carlo computer simulation study is presented to discuss the extension of flexible, linear polymer chains due to the presence of equally flexible side chains. We consider the enhancement of the persistence length of bottle-brush structures in an athermal solution due to steric interactions between the side chains, The largest structure studied consists of a backbone of 100 beads with 50 side chains of 20 beads each, The persistence length lambda is evaluated in two different ways using the radius of gyration of the backbone and the bond angle correlation function, respectively. A correct description of the backbone conformations is shown to require at least two characteristic lengths. At a small len...