Let τ be a premeasure on a complete separable metric space and let τ* be the Method I measure constructed from τ. We give conditions on τ such that τ* has a regularity as follows: Every τ*-measurable set has measure equivalent to the supremum of premeasures of its compact subsets. Then we prove that the packing measure has this regularity if and only if the corresponding packing premeasure is locally finite.