Our studies on gas trapping in amorphous water ice at 24-100 K were extended, by using mixtures of CH4, CO, N2, and Ar, rather than single gases. In 1:1 gas:(water vapor) mixtures, the competition among these gases on the available sites in the ice showed that the trapping capacity for the various gases is determined not only by the structure and dynamics of the ice, but is also influenced by the gas itself. Whereas at 24-35 K all four gases are trapped in the ice indiscriminantly, at 50-75 K there is a clear enhancement, in the order of CH4 > CO > N2 > or approximately Ar. This order is influenced by the gas-water interaction energy, the size of the trapped gas atom or molecule, the type of clathrate-hydrate formed (I or II) and, possibly, other factors. It seems that the gas can be trapped in the amorphous ice in several different locations, each being affected in a different way by the deposition temperature and gas composition. Once a gas atom or molecule is trapped in a specific location, it is predestined to emerge in one of eight different temperature ranges, which are associated with changes in the ice. The experimentally observed enhancements, together with the findings on the gas composition of comet Halley, might enable an estimation of the gas composition in the region of comet formation.