We discuss features of coronal mass ejections (CMEs) that are specific to heliospheric observations at large elongation angles. Our analysis is focused on a series of two eruptions that occurred on 2007 January 24-25, which were tracked by the Heliospheric Imagers (HIs) on board STEREO. Using a three-dimensional (3D) magnetohydrodynamic simulation of these ejections with the Space Weather Modeling Framework (SWMF), we illustrate how the combination of the 3D nature of CMEs, solar rotation, and geometry associated with the Thomson sphere results in complex effects in the brightness observed by the HIs. Our results demonstrate that these effects make any in-depth analysis of CME observations without 3D simulations challenging. In particular, the association of bright features seen by the HIs with fronts of CME-driven shocks is far from trivial. In this Letter, we argue that, on 2007 January 26, the HIs observed not only two CMEs, but also a dense corotating stream compressed by the CME-driven shocks.