  Stationary axisymmetric binary systems of unequal counterrotating Kerr-Newman
sources with a massless strut in between are studied. By means of the choice of
a suitable parametrization, the axis conditions and the absence of individual
magnetic charges are fulfilled; thus, the entire metric reduces to a
6-parametric asymptotically flat exact solution. Later on, with the purpose to
describe interacting black holes, the analytic functional form of the horizon
half-length parameter $\sigma_{k}$ is obtained explicitly in terms of physical
Komar parameters: mass $M_{k}$, electric charge $Q_{k}$, angular momentum
$J_{k}$, and coordinate distance $R$, where the seven physical parameters
satisfy a simple algebraic relation. Finally, in the limit of extreme black
holes, the full metric is derived in a closed analytical form, and a study on
the absence or appearance of naked singularities off the axis is presented.
