Several methods have been proposed for dedicated SPECT imaging of the breast. Two key characteristics achieved by these methods are shortened distance and lessened attenuation between the SPECT collimator and the breast. However, many of these methods are unable to image the important regions of the axilla and upper chest. Partial-Circle pinhole trajectories can image into the axilla, but only over a narrow axial range. Here we propose X and X-Line trajectories that can effectively image a broad axial range of the breast, axilla, and upper chest. The X and X-Line trajectories provide a third dimension of pinhole displacement, which is key to expanding the range of sufficient sampling. In order to investigate spatial variations in the imaging characteristics of different pinhole trajectories, phantoms were constructed with hot lesions and Defrise slabs distributed throughout the breast and torso. Projection data were computer simulated, and images were reconstructed by OSEM. These studies indicate that all three trajectories can sample activity well into the axilla. However, the axial range of good sampling is narrow with the Partial-Circle trajectory. The X and X-Line trajectories provide good sampling well into the axilla and over a broad axial range. The convex hulls of the X and X-Line trajectories encompass the breast and much of the axilla and upper chest, thereby satisfying Tuy's condition for sufficient sampling of those regions, truncation issues aside. The spatial extent of the convex hull is tunable. At the same time, the X and X-Line trajectories achieve two other key characteristics of dedicated SPECT breast imaging: Shortened average distance and lessened average attenuation between the collimator, i.e. the pinhole, and the breast and other nearby tissue of interest.