We bound the number of electrons \( Q \) that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizsäcker functional: instead of the classical power 5/3 more general powers \( p \) are considered. For \( 3/2 < p < 2 \) we prove the excess charge conjecture, i.e., that \( Q \) is uniformly bounded in the atomic number \( Z \). The case \( p = 3/2 \) is critical: the behavior changes from a uniform bound in \( Z \) to a linear bound at the critical coupling \( 4 \sqrt{\pi} \) of the nonlinear term. We also improve the linear bound for all \( p \geq 6/5 \). This is joint work with Heinz Siedentop, LMU, Munich.