Subsalt imaging has been a challenge for Gulf of Mexico (GoM) exploration, mostly due to the complexity of salt geometry and high salt-sediment velocity contrast. In addition to these, the presence of inclusions within the salt, also referred to as dirty salt, presents an additional significant challenge in subsalt imaging. Following a systematic study with synthetic datasets, we propose a new method for automatically determining the dirty salt geometry, and a further consolidated constrained iterative dirty salt velocity model building flow. We applied this workflow on a real GoM dataset and demonstrate its effectiveness by presenting an improved subsalt image.