The effect of surface roughness on phonon transport in a nanowire has often been described by treating the surface as flat with a specularity parameter (p)(p) in the range between 0 and 1. A lower thermal conductivity limit is approached at p=0p=0 for diffuse surface. It is demonstrated here by Monte Carlo simulation that sawtooth roughness on a nanowire can cause phonon backscattering and suppress the thermal conductivity below the diffuse surface limit. The backscattering effect can be accounted for only by a negative ppif the detail of the surface roughness is ignored.