The effective thermal conductivity of non-continuum wires with rough boundaries was investigated theoretically. The boundaries were designed to reflect phonons differently depending on the phonon frequency or the angle of incidence. Devices with these properties could be useful in thermal management problems on the nanoscale and microscale. In the first study the scattering was dependent on the frequency of the phonons where lower frequency phonons reflected diffusely while higher frequency phonons reflected specularly. In the directional study a parameter p, which is a function of the x-component of direction and the phonon frequency, was used to account for the degree of specularity. This work studied the effects of varying the cutoff frequency and the device size, including length and cross section. A one-dimensional Monte Carlo simulation of phonon transport was used to investigate the thermal conductivity of a device with adiabatic boundaries. This difference in scattering emerges from the geometry and magnitude of rough surfaces where the roughness is of the order of the dominant phonon wavelength.