The recent 2007-2009 weak and long solar minimum offers unique possibilities for gaining new insights into the physics of cosmic-ray transport. This cycle was distinctly different from earlier 'typical' cycles. Galactic and anomalous cosmic rays (GCRs and ACRs), whose solar-cycle variation do typically track each other quite closely (with proper scaling factors) behaved quite differently: GCRs reached record-high level in 2009, while ACR fluxes remained below their maximum 22 years earlier, suggesting that the source spectrum of the accelerated ACRs at the TS was lower. We may anticipate a similarly quiet solar minimum with the important difference, that the Sun has reversed its magnetic polarity. The present work focuses on possible effects on ACR acceleration connected with particle drifts in the large-scale heliospheric magnetic field (HMF). The roles of the pole-to-equator electric potential and the wavy heliospheric current sheets (HCS) are addressed. Drift effects due to the wavy HCS are simulated by employing a 2D axially symmetric 'hoop-model', which keeps computations at a comfortable level, while still captures the robust effects of the 3D wavy HCS. The preliminary results presented here are qualitative and are not yet intended for quantitative agreement with observations.