Shortening paths in the Bash prompt with PROMPT_DIRTRIM

Bash 4 introduced a new environment variable called PROMPT_DIRTRIM that allows the shortening of paths displayed in its prompts (via w in PS1. I added

PROMPT_DIRTRIM=3

to my ~/.bashrc and whereas Bash used to display this prompt:

[user@host /media/D/Projects/nitdroid/ul/out/target/product/generic/system/framework]$

It now displays

[user@host .../generic/system/framework]$

which is a huge improvement especially when working with deep directory structures.