  We explicitly determine the locations of G orbifold conformal field theories,
G=Z_M, M=2,3,4,6, G=\hat D_n, n=4,5, or G the binary tetrahedral group \hat T,
within the moduli space M^{K3} of N=(4,4) superconformal field theories
associated to K3. This is achieved purely from the known description of the
moduli space [AM94] and the requirement of a consistent embedding of orbifold
conformal field theories within M^{K3}. We calculate the Kummer type lattices
for all these orbifold limits. Our method allows an elementary derivation of
the B-field values in direction of the exceptional divisors that arise from the
orbifold procedure [Asp95,Dou97,BI97], without recourse to D-geometry. We show
that our consistency requirement fixes these values uniquely and determine them
explicitly. The relation of our results to the classical McKay correspondence
is discussed.
