The differential cross section d σ d t′ for the charge-exchange process π + p → π 0 ( π + p) at 8, 16 and 23 GeV/ c is presented for several regions of the π + p effective mass. It is found that the dip at t ′ ≈ 0.6 (GeV/ c ) 2 which is observed in the Δ(1236) mass band becomes a less pronounced structure in the higher mass regions. However, while the slope of the d σ d t′ distributions in the near-forward direction decreases strongly with increasing π + p mass, there is no evidence that the observed structure moves to higher values of t ′ as the π + p mass increases. These results are consistent with a Regge-exchange picture where the position of the dip is determined by the exchanged trajectory, but are inconsistent with a simple geometrical picture.