Much attention has been focused on the reaction of the magnetosphere to the solar wind during the recent extended solar minimum (2006–2010). Although this period was exceptionally quiet when categorized by some parameters (e.g., the number of sunspots) the solar wind still contained features which impacted the Earth's magnetosphere and caused geomagnetic disturbances. Recurrent corotating interaction regions (CIRs) and associated high-speed solar wind streams (HSSs) are typically associated with the declining phase of the solar cycle and were a regular feature of the solar wind during the most recent solar minimum. Here we compare and contrast strong and weak HSSs in the solar wind and their subsequent effect within the Earth's magnetosphere. We find significant differences between strong and weak HSS effects in the plasmasphere, in the ion and electron plasma sheets, and in the outer electron radiation belt. A density-temperature description of the outer radiation belt is shown to shed light on why the radiation belt flux is observed to return at a higher level after the arrival of strong HSSs than before strong HSSs and why the flux is observed to return at a lower level after the arrival of weak HSSs than before weak HSSs.