Question on minibuffer editing

[Arvind Kumar]

Hi Guys,
   Say, for example, I am opening a file in emacs using C-x f. I am in
one directory with long hierarchy. I want to go down the hierarchy to
some other path. Keep pressing the backspace button is cumbursome. How
do I set the key so that c-backspace or Alt-backspace deletes the word
in the minibuffer??? I am sure I was it's possible because i had this
setting in my last company. But I can't remember exactly what this
setup was!!!

Any help will be appreciated!!
Arvind Kumar