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Electrons in strong magnetic fields can be described by one-dimensionalmodels in which the Coulomb potential and interactions are replaced byregularizations associated with the lowest Landau band. For a large class ofmodels of these type, we show that the maximum number of electrons that can bebound is less than a Z + Z f(Z). The function f(Z) represents a smallnon-linear growth which is quadratic in log Z when the magnetic field strengthgrows polynomially with the nuclear charge Z. In contrast to earlier work, themodels considered here include those arising from realistic cases in which thefull trial wave function for N-electrons is the product of an N-electron trialfunction in one-dimension and an antisymmetric product of states in the lowestLandau level.Comment: Submitted to special issue of J. Stat. Phys. in honor of E. Lieb's  70th birthday. (latex, 25 pages

One-Dimensional Models for Atoms in Strong Magnetic Fields, II: Anti-Symmetry in the Landau Levels