  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.
