Abstract: There is a reduced group of Ce very heavy Fermions (VHF) which do not order magnetically down to at least T ≈ 500 mK because they are very close to a T_ord = 0 critical point. These compounds are at the top of the lim_{T→ 0} C_m/T specific heat values because they collect very high density of low energy excitations. From the analysis of C_m(T)/T and entropy S_m(T) dependencies performed on selected CePd₃M_x ternaries (where M = B and Be) a quantitative evaluation of an upper limit for the density of excitations can be proposed. These observations exclude any evidence of C_m(T)/T divergency as T→ 0 in agreement with thermodynamic laws. A comparison with selected Yb-base VHF supports these features.