We investigate the mechanical properties of amorphous polymers by means of coarse-grained simulations and nona ne lattice dynamics theory. A small increase of polymer chain bending sti ness leads rst to softening of the material, while hardening happens only upon further strengthening of the backbones. This nonmonotonic variation of the storage modulus G0 with bending sti ness is caused by a competition between additional resistance to deformation o ered by sti er backbones and decreased density of the material due to a necessary decrease in monomer-monomer coordination. This counter-intuitive nding suggests that the strength of polymer glasses may in some circumstances be enhanced by softening the bending of constituent chains.