We consider the propagation of type I open superstrings on orbifolds w
ith four non-compact dimensions and N = 1 supersymmetry. In this paper
, we concentrate on a non-trivial Z(2) x Z(2) example. We show that co
nsistency conditions, arising from tadpole cancellation and algebraic
sources, require the existence of three sets of Dirichlet 5-branes. We
discuss fully the enhancements of the spectrum when these 5-branes in
tersect. An amusing attribute of these models is the importance of the
tree-level (in type I language) superpotential to the consistent rela
tionship between Higgsing and the motions of 5-branes.