Smoothing out surfaces obtained through displacement modifier I'm inspecting ways to smooth things correctly in Blender. I've created this structure out of a cube and displacement modifiers applied to every side. As you can see, results bear some grid artifacts:



My question: is there a way of smoothing that out of the usual subsurf modifier? 
I've used procedural textures over vertex groups to create displacement.
Maybe there is a way to obtain smoother geometry by using finer textures in the beginning...
I could resort to some smooth modifier, but there are three of them and the difference is not really clear to me...
Thank you in advance.

the .blend file
Seeing nobody answering, I'll post something myself:



Obviously, used subsurf.
I'll be checking in other ways when I have some more time...