Based on numerical evidence and theoretical arguments, we demonstrate that the unconventional density variations are not really unconventional and should be included in the density variational domain of any ground-state density. As a result, Lieb's Theorem 3.10 (Lieb, Int J Quantum Chem 1983, 24, 243) is reconfirmed. More specifically, the energy variation delta E-v is of order higher than linear order of the density variation delta n(r) about the ground-state density n(0)(r) of a system with a fixed number of electrons in Hilbert space, whereas delta E-v is of linear order of delta n(r) about the ground-state density of a system with a varied number of electrons in Fock space. The unconventional density variations are not the cause for the linear-order behavior of delta E-v in Fock space and the derivative discontinuity of the total energy. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 3199-3216, 2009