I have a List of objects which are ordered. I would like to remove redundant objects where redundant does not necessarily mean duplicate. Here is an example:

List<Point> points = new List<Point>
{
   new Point(0, 10),
   new Point(1, 12),
   new Point(2, 16),
   new Point(3, 16),
   new Point(4, 16),
   new Point(5, 13),
   new Point(6, 16),
};

I am interested in removing the new Point(3, 16) entry because it doesn't provide useful information; I already know that the element at 2=16 and the element at 4=16. The information that 3=16 doesn't do me any good in my application (because I already have the bounds {2,4}=16), so I would like to remove that entry. I'd also like to not that I want to keep the 5th and 6th entry because there are not consecutive entries where Y=16.

Is there a slick way to do this with linq?