The ATHENA and ATRAP collaborations have recently created large numbers of untrapped anti-hydrogen atoms. The most commonly suggested scheme for trapping the anti-hydrogen is to use a Minimum-B trap. Unfortunately, the Minimum-B fields are very likely to destroy the confinement of the anti-hydrogen constituents, the positrons and anti-protons, which are themselves held in double-well Malmberg-Penning traps. The reasons for the loss of confinement, and modifications to the Minimum-B trap that may alleviate this problem, are discussed in this paper. (C) 2003 Elsevier B.V. All rights reserved.