The passage of Ulysses through the high-latitude inner heliosphere has provided an opportunity to study both the three-dimensional structure of the heliosphere and also the 0.7-6 MeV nucleon(-1) component of the anomalous cosmic rays. We have found that within the streamer belt (less than or similar to 20 degrees) the particle fluxes are significantly enhanced compared with those in the high-latitude region, which constitutes the main focus of this work. Once Ulysses left the streamer belt in mid-1992, the southern heliosphere at radial distances greater than or similar to 1 AU was found to be dominated by a recurrent corotating interaction region (CIR). This region had a complex effect on the charged particle populations at high heliolatitude. On the one hand, the forward and reverse shocks associated with the CIR were the principal source of energetic ions up to similar to 1 MeV nucleon(-1) and electrons up to similar to 100 beV. On the other, these CIRs were also very effective at modulating charged particles at higher energies entering the inner heliosphere from large distances; these modulation effects were observable at Ulysses even at high latitudes when the CIR itself was not detected locally. By careful consideration of the low-energy (40-65 keV) electron fluxes, we are able to distinguish times when Ulysses was well connected to the CIR shocks and times when it was not. Thus, we are able to separate ions originating from the CIR and those from beyond the CIR, and hence we are able to extend the anomalous cosmic-ray spectrum to lower energies than has hitherto been possible. At the upper end of the Heliosphere Instrument for Spectra, Composition, and Anisotropy and Low Energies (HI-SCALE) energy range (greater than or similar to 2 MeV nucleon(-1)), the anomalous cosmic rays dominate even when the connection is to the CIR, and we are able to determine directly the amount of modulation imposed by the CIR. These analyses confirm that the anomalous component of the medium-mass ions must originate from the distant heliosphere. We find for the first time clear evidence of an anomalous component in the carbon spectrum in the inner heliosphere. There is a latitudinal gradient of 1.35% +/- 0.5% deg(-1) for the anomalous oxygen in the 2-6 MeV nucleon(-1) range. We do not find a detectable component of less than or equal to 2.8 MeV nucleon(-1) helium from the distant heliosphere.