We compute atomistically the heat conductance for ultrathin pristine silicon nanowires (SiNWs) with diameters ranging from 1 to 5 nm. The room temperature thermal conductance is found to be highly anisotropic: wires oriented along the 110 direction have 50−75% larger conductance than wires oriented along the 100 and 111 directions. We show that the anisotropies can be qualitatively understood and reproduced from the bulk phonon band structure. Ab initio density functional theory (DFT) is used to study the thinnest wires, but becomes computationally prohibitive for larger diameters, where we instead use the Tersoff empirical potential model (TEP). For the smallest wires, the thermal conductances obtained from DFT and TEP calculations agree within 10%. The presented results could be relevant for future phonon-engineering of nanowire devices.