We generalize a recent result of Rossi and Valla, and independently Wang, about the depth ofG(m) where m is the maximal ideal of ad-d imensional Cohen-Macaulay local ringRhaving embedding dimesionThe generalization removes the restriction on the embedding dimension and replaces it with the condition thatwhereJis ad-generated minimal reduction ofm. The main theorem also applies tom-primary idealsIsatisfying, whereJis ad-generated reduction ofI. An example of such an / in a 5-dimensional regular local ring is included as a nontrivial illustration of tie theorem.