When it comes to finding the right word to describe smoothing down hair or fur, there are many synonyms to choose from. Some synonyms for the phrase "slick down" include "smooth", "flatten", "press", "polish", "tame", and "constrain". Each of these words describes the action of flattening or smoothening hair or fur. However, they may differ in the level of force required and the impact on the texture of the hair or fur. In the end, selecting the right synonym for "slick down" depends on the context in which it is used and the desired effect needed to achieve a particular style or look.