Abstract Both the recent 2009 and 2020 solar minima were classified as unusually quiet and characterized with unusually high galactic cosmic-ray (GCR) levels. However, unlike the trends from previous decades, in which anomalous cosmic-ray (ACR) and GCR levels strongly agreed, the ACR intensities did not reach such high, record-setting levels. This discrepancy between the behavior of GCRs and ACRs is investigated in this work by simulating the acceleration and transport of GCR and ACR oxygen under different transport conditions. After using recent observations to constrain any remaining free parameters present in the model, we show that less turbulent conditions are characterized by higher GCR fluxes and lower ACR fluxes, due to less efficient ACR acceleration at the solar wind termination shock. We offer this as an explanation for the ACR/GCR discrepancy observed during 2009 and 2020, when compared to previous solar cycles.