Contrast-enhanced dual energy digital breast tomosynthesis (CE-DE-DBT) is designed to image iodinated masses while suppressing breast anatomical background. Scatter is a problem, especially for high energy acquisition, in that it causes severe cupping artifact and iodine quantitation errors. We propose a patient specific scatter correction (SC) algorithm for CE-DE-DBT. The empirical algorithm works by interpolating scatter data outside the breast shadow into an estimate within the breast shadow. The interpolated estimate is further improved by operations that use an easily obtainable (from phantoms) table of scatter-to-primary-ratios (SPR)--a single SPR value for each breast thickness and acquisition angle. We validated our SC algorithm for two breast emulating phantoms by comparing SPR from our SC algorithm to that measured using a beam-passing pinhole array plate. The error in our SC computed SPR, averaged over acquisition angle and image location, was about 5%, with slightly worse errors for thicker phantoms. The SC projection data, reconstructed using OS-SART, showed a large degree of decupping. We also observed that SC removed the dependence of iodine quantitation on phantom thickness. We applied the SC algorithm to a CE-DE-mammographic patient image with a biopsy confirmed tumor at the breast periphery. In the image without SC, the contrast enhanced tumor was masked by the cupping artifact. With our SC, the tumor was easily visible. An interpolation-based SC was proposed by (Siewerdsen et al 2006 Med. Phys. 33 187-97) for cone-beam CT (CBCT), but our algorithm and application differ in several respects. Other relevant SC techniques include Monte-Carlo and convolution-based methods for CBCT, storage of a precomputed library of scatter maps for DBT, and patient acquisition with a beam-passing pinhole array for breast CT. Our SC algorithm can be accomplished in clinically acceptable times, requires no additional imaging hardware or extra patient dose and is easily transportable between sites.