Digital breast tomosynthesis (DBT) captures some depth information and thereby improves the conspicuity of breast lesions, compared to standard mammography. Using contrast during DBT may also help distinguish malignant from benign sites. However, adequate visualization of the low iodine signal requires a subtraction step to remove background signal and increase lesion contrast. Additionally, attention to factors that limit contrast, including scatter, noise, and artifact, are important during the image acquisition and post-acquisition processing steps. Stationary DBT (sDBT) is an emerging technology that offers a higher spatial and temporal resolution than conventional DBT. This phantom-based study explored contrast-enhanced sDBT (CE sDBT) across a range of clinically-appropriate iodine concentrations, lesion sizes, and breast thicknesses. The protocol included an effective scatter correction method and an iterative reconstruction technique that is unique to the sDBT system. The study demonstrated the ability of this CE sDBT system to collect projection images adequate for both temporal subtraction (TS) and dual-energy subtraction (DES). Additionally, the reconstruction approach preserved the improved contrast-to-noise ratio (CNR) achieved in the subtraction step. Finally, scatter correction increased the iodine signal and CNR of iodine-containing regions in projection views and reconstructed image slices during both TS and DES. These findings support the ongoing study of sDBT as a potentially useful tool for contrast-enhanced breast imaging and also highlight the significant effect that scatter has on image quality during DBT.