It is shown that the controversy over the item-vs-parcel factoring as commonly understood admits of solution and reconciliation by the new method of radical parcelling. Items have the defect of instability and blurred hyperplanes. Parcels as commonly used also have defects. Radial parcelling, avoiding the subjectivity and uneven sized in ordinary packaging, is shown theoretically to yield the same common factor space and better simple structure. Reference to data set out in detail elsewhere indicated that such parcelled factoring in fact yields essentially the same factor space and the same factors as does item factoring and that the replicability across two radial parcel factorings is high. Although the method involves, in principle, a double-factoring, it is not necessary to rotate the large item factored matrix, and thus there is generally a gain in time over a single item factoring.