I'll always be looking for fibre in my diet, particularly soluble fibre. I'm a big fan of Mark's Daily Apple which discusses Gut Sense/Fibre Menace ideas.
http://www.marksdailyapple.com/forum/thread65706.html

...particularly this indepth response, if you're interested:
http://medcapsules.com/forum/showthread.php?tid=2665

Low fibre diets are usually prescribed pre or post surgery or for conditions like Crohn's Disease.

I do not believe a low carb healthy fat woe is mutually exclusive from healthy fibre in a diet.