  We give a new definition of the so-called overgenerated rings, which are the
usual tool used to define the asymptotic structure of a (C,E,P)-algebra,
written as a factor space M_{(A,E,P)}/N_{(I_{A},E,P)}. With this new definition
and in the particular case of E=C^{&#8734;}, we show that a moderate element
i.e. in M_{(A,E,P)} is negligible if and only if it satisfies the
C&#8304;-order estimate for the ideal N_{(I_{A},E,P)}.
