The pulsation parallax method, or Baade-Wesselink method (BW), is a powerful way to measure distances to Cepheids in a pseudo-geometric way. In the quest for obtaining the most precise distance using long baseline interferometry (we reached 1.5%), we obtained two maybe not so unsuspected results. First of all, our studies show that we reached a point where the assumption that the pulsating photosphere can be approximated using static models is not valid in the context of the BW method. Secondly, we unveiled the systematic presence of Circum Stellar Envelopes (CSE) at a few stellar diameters scale, as a slight near-infrared excess, which could be an indication that mass loss is currently taking place. Not only these two results represent biases to the BW method, and deserve to be observationally studied, they also shed new lights on our knowledge of the Cepheids themselves and call for extensive modeling.