Accurate space weather forecasting requires knowledge of the trajectory of coronal mass ejections (CMEs), including any deflections close to the Sun or through interplanetary space. Kay et al. (2013) introduced ForeCAT, a model of CME deflection resulting from the background solar magnetic field. For a magnetic field solution corresponding to Carrington Rotation (CR) 2029 (declining phase, April-May 2005), the majority of the CMEs deflected to the Heliospheric Current Sheet (HCS), the minimum in magnetic pressure on global scales. Most of the deflection occurred below 4 R . Here we extend ForeCAT to include a three dimensional description of the deflecting CME. We attempt to answer the following questions: a) Do all CMEs deflect to the magnetic minimum? and b) Does most deflection occur within the first few solar radii ( 4 R )? Results for solar minimum and declining phase CMEs show that not every CME deflects to the magnetic minimum and that the deflection is typically determined below 2 R . Slow, wide, low mass CMEs in declining phase solar backgrounds with strong magnetic field and magnetic gradients exhibit the largest deflections. Local gradients related to active regions tend to cause the largest deviations from the deflection predicted by global magnetic gradients, but variations can also be seen for CMEs in the quiet sun regions of the declining phase CR. We show the torques due to differential forces along the CME can cause rotation about the CME's toroidal axis.