We have investigated the relationship between the energetic (~1 MeV) proton intensity (J) and the magnetic compression ratio (C) measured at the trailing edges of corotating interaction regions observed at Ulysses. In general, our results show that the proton intensity was well correlated with the compression ratio, provided that the seed intensity remained constant, consistent with predictions of the Fermi model. Specifically, our results indicate that particles were accelerated to above ~1 MeV in energy at or near the trailing edges of the compression regions observed in the midlatitude southern heliosphere, irrespective of whether the bounding reverse shocks were present or not. On the basis of this, we conclude that shock acceleration is probably not the only mechanism by which particles are accelerated to above ~1 MeV in energy at compression or interaction regions (CIRs). On the basis of magnetic field measurements obtained near the trailing edges of several midlatitude CIRs, we propose that particles could have been accelerated via the Fermi mechanism by being scattered back and forth across the trailing edges of the compression regions by large-amplitude Alfv¿n waves. Our results also show that the proton intensity was well correlated with the compression ratio during low solar activity periods but was essentially independent of C during periods of high solar activity. We suggest that the correlation between J and C was not observed during solar active periods because of significant variations in the seed intensity that result from sporadic contributions from transient solar events. In contrast, the correlation was observable during quiescent periods probably because contributions from transients had decreased dramatically, which allowed the CIRs to accelerate particles out of a seed population whose intensity remained relatively unperturbed. ¿ 1998 American Geophysical Union