We present a technique that can be used to generate a static, axisymmetric
solution of the Einstein-Maxwell-dilaton equations from a stationary, axisy
mmetric solution of the vacuum Einstein equations. Starting from the Kerr s
olution, Davidson and Gedalin have previously made use of this technique to
obtain a pair of oppositely charged, extremal dilatonic black holes, known
as a black dihole. In this paper, we shall instead start from the Kerr-NUT
(Newman-Unti-Tamburino) solution. it will be shown that the new solution c
an also be interpreted as a dihole, but with the black holes carrying unbal
anced magnetic charges. The effect of the NUT parameter is to introduce a n
et magnetic charge into the system. Finally, we uplift our solution to ten
dimensions to describe a system consisting of D6 and anti-D6-branes with un
balanced charges. The limit in which they coincide agrees with a solution r
ecently derived by Brax et al.