  The impact of a (I=0, J^P=1/2^+) Z^+(1540) resonance with a width of 5 MeV or
more on the K+N (I=0) elastic cross section and on the P01 phase shift is
examined within the KN meson-exchange model of the Juelich group. It is shown
that the rather strong enhancement of the cross section caused by the presence
of a Z^+ with the above properties is not compatible with the existing
empirical information on KN scattering. Only a much narrower Z^+ state could be
reconciled with the existing data -- or, alternatively, the Z^+ state must lie
at an energy much closer to the KN threshold.
