How to fix ugly lines in my mesh? I would like my mesh to achieve similar shape (helmet) like this:



The mesh:

I know my mesh is far away from look like what I want, but I'm kinda newbie so I'm trying the best with what I got.

Without subsurf (just for let you know how it looks without it):



Base mesh with subsurf:





How can I get rid of those weird and ugly lines or achieve similar form?

Thank you for helping guys!, got something similar @Manu Järvinen , @Leander, @miceterminator
EDIT: haha, Leander beat me to it by 3 minutes with the same kind of answer :)

For the reference image type of helmet (a stretched sphere) I definitely would start with a cube that has Subsurf modifier applied:





After that, just add a new Subsurf modifier to it and it's smooth as silk and still quite easily editable: