There have been two distinct schemes studied in the literature for instanton counting in A(p-1) asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes - namely the counting of orbifolded instantons and instanton counting in the resolved space - lead in general to different results for partition functions. We illustrate this observation in the case of N = 2 U(N) gauge theory with 2N flavors on the A(p-1) ALE space. We propose simple relations between the instanton partition functions given by the two schemes and test them by explicit calculations.