Energetic ions associated with the forward and reverse shocks of corotating interaction regions (CIRs) are commonly observed at places within CIRs that are not magnetically connected to either shock. Examples have been documented with data from Pioneer 10 and 11 and Ulysses. They pose a problem for models that account for these shock-associated, corotating energetic ion populations (CEIPs) in terms of ion energization at the shocks followed by ion propagation along field lines. According to these models, regions magnetically unconnected to a shock should contain no shock-associated ions. Cross-field diffusion has been suggested as a mechanism for populating the shock-unconnected regions of CIRs. Here we quantitatively examine this suggestion. We use the Green's function solution to the convection-diffusion equation applied to idealized CIR geometry, with a source at the reverse shock, to compute the ratio of the ion flux in the heart of a CIR to the flux in the shock-connected part of the CIR and to compare the result with typical ratios observed by the Pioneer spacecraft. The computed ratio for resonant diffusion is many orders of magnitude below the observed ratio. For stochastic field line diffusion, the computed ratio is many orders of magnitude above the observed ratio if a diffusion coefficient appropriate to the free solar wind is used. It agrees with the observed ratio, however, if a reduced diffusion coefficient appropriate to CIRs is used. We conclude that the stochastic field model of cross-field diffusion can account for the presence of energetic ions in regions of CIRs that are magnetically unconnected to shock waves. ¿ American Geophysical Union 1995