We studied two InAs/InP quantum wire samples with different growth conditions. The photoluminescence of the first sample reveals up to six distinct peaks, while the second has only two pronounced photoluminescence peaks that are attributed to flat wires with heights that differ by exactly one monolayer. Despite the large band offsets in this system, the photoluminescence energy shift of these peaks with a magnetic field applied in the plane of the wires shows that the extent of the exciton wave function in the growth direction is much larger than the wire height, i.e. the wave function spills over into the InP. Moreover, the exciton wave function shrinks for increasing wire height. The wave function spill-over is qualitatively confirmed in the first quantum wire sample. (C) 2003 Elsevier B.V. All rights reserved.