The relative incompatibility of Ar and K are fundamental parameters in understanding the degassing history of the mantle. Clinopyroxene is the main host for K in most of the upper mantle, playing an important role in controlling the K/Ar ratio of residual mantle and the subsequent time-integrated evolution of 40Ar/36Ar ratios. Clinopyroxene also contributes to the bulk Ar partition coefficient that controls the Ar degassing rate during mantle melting. The partitioning of Ar and K between clinopyroxene and quenched silicate melt has been experimentally determined from 1 to 8 GPa for the bulk compositions Ab80Di20 (80 mol% albite-20 mol% diopside) and Ab20Di80 with an ultraviolet laser ablation microprobe (UVLAMP) technique for Ar analysis and the ion microprobe for K. Data for Kr (UVLAMP) and Rb (ion probe) have also been determined to evaluate the role of crystal lattice sites in controlling partitioning. By excluding crystal analyses that show evidence of glass contamination, we find relatively constant Ar partition coefficients (DAr) of 2.6 × 10-4 to 3.9 × 10-4 for the Ab80Di20 system at pressures from 2 to 8 GPa. In the Ab20Di80 system, DAr shows similar low values of 7.0 × 10-5 and 3.0 × 10-4 at 1 to 3 GPa. All these values are several orders of magnitude lower than previous measurements on separated crystal-glass pairs. DK is 10 to 50 times greater than DRb for all experiments, and both elements follow parallel trends with increasing pressure, although these trends are significantly different in each system studied. The DK values for clinopyroxene are at least an order of magnitude greater than DAr under all conditions investigated here, but DAr appears to show more consistent behavior between the two systems than K or Rb. The partitioning behavior of K and Rb can be explained in terms of combined pressure, temperature, and crystal chemistry effects that result in changes for the size of the clinopyroxene M2 site. In the Ab20Di80 system, where clinopyroxene is diopside rich at all pressures, DK and DRb increase with pressure (and temperature) in an analogous fashion to the well-documented behavior of Na. For the Ab80Di20 system, the jadeite content of the clinopyroxene increase from 22 to 75 mol% with pressure resulting in a contraction of the M2 site. This has the effect of discriminating against the large K+ and Rb+ ions, thereby countering the effect of increasing pressure. As a consequence Dk and DRb do not increase with pressure in this system. In contrast to the alkalis (Na, K, and Rb), DKr values are similar to DAr despite a large difference in atomic radius. This lack of discrimination (and the constant DAr over a range of crystal compositions) is also consistent with incorporation of these heavier noble gases at crystal lattice sites and a predicted consequence of their neutrality or "zero charge." Combined with published DAr values for olivine, our results confirm that magma generation is an efficient mechanism for the removal of Ar from the uppermost 200 km of the mantle, and that K/Ar ratios in the residuum are controlled by the amount of clinopyroxene. Generally, Ar is more compatible than K during mantle melting because DAr for olivine is similar to Dk for clinopyroxene. As a result, residual mantle that has experienced variable amounts of melt extraction may show considerable variability in time-integrated 36Ar/40Ar.