Bent Edges near Vertices after using Knife Tool - Can I smooth?

Hey. I’m fairly new to blender and I am modeling the “Captain Blender” from a book, and I am having issues with some bent edges at some vertices after using the knife tool. it makes it quite annoying to work with when they are like this. I want to know if there is a way to “smooth” out these edges.

I have a mirror and subsurf modifier on this model. The attached images show what this looks like with the subsurf modifier off and on in edit mode.

Add two additional cuts

For the subsurf modifier try and always use quads

Thanks Richard! This book occasionally skips some key concepts. Also, it seems that version they are using (2.6 something, I think), has a different knife tool then the one in 2.7.

The blender mesh system was changed in blender 2.63. This changed the knife tool functionality.
Before blender 2.63 you could only create faces with 3 or 4 sides. Since blender 2.64 you can now create faces with >4 sides. Watch out during modelling you stay with triangles and quads