Under the intrinsic coregionalization model, if both primary and secon
dary measurements are available at all sample locations, the conventio
nal geostatistical wisdom is that cokriging provides exactly the same
solution as univariate kriging on the primary process alone. However,
recent examples have been given where nonzero secondary cokriging weig
hts have occurred under this spatial dependence structure. This note i
dentifies the conditions under which secondary information is useful u
nder the assumption of intrinsic coregionalization. An illustration is
given using a dataset of plutonium and americium concentrations colle
cted from a region of the Nevada Test Site.