Recently Gimon and Johnson and Dabholkar and Park have constructed typ
e I theories on K3 orbifolds. The spectra differ from that of type I o
n a smooth K3, having extra tensors. We show that the orbifold theorie
s cannot be blown up to smooth K3's, but rather Z(2) orbifold singular
ities always remain. Douglas's recent proposal to use D-branes as prob
es is useful in understanding the geometry. The Z(2) singularities are
of a new type, with a different orientifold projection from those pre
viously considered. We also find a new world-sheet consistency conditi
on that must be satisfied by orientifold models.