The volatile inventories of planets depend on the precise partitioning of different volatiles between the gas and solid phases across the planet birth disk. For the case of hyper-volatiles (e.g., CO, N2, and noble gases), the partitioning also depends on how efficiently they are trapped into less volatile ice matrices. The thicknesses of these ice matrices can range from a few molecular layers to macroscopic bodies, and in this study we explore how entrapment efficiency depends on the ice thickness between tens of nanometers and a few micrometers (∼50–3000 monolayers, ML). We carry out a series of temperature-programmed desorption (TPD) experiments on H2O:CO and CO2:CO mixtures with 5:1 and 15:1 matrix-to-CO mixing ratios. Entrapment efficiencies range from 41% to 64%, with higher entrapment efficiencies for the more dilute ices. Surprisingly, we find no significant difference in entrapment across the studied ice thicknesses for either H2O or CO2 ice matrices. Complementary TPD experiments with the additional hyper-volatiles N2 and Ar see a similar trend with ice thickness. We speculate that these results may be due to surface topography such as cracks that lead to hyper-volatile escape from deep ice layers. In either case, these experiments show that entrapment in microscopic ices is relatively insensitive to ice thickness (above ∼50 ML). In protoplanetary disks we therefore expect efficient entrapment in icy grains of a range of grain sizes.