I found tinyCAD addon the most helpful solution for this problem. It can be downloaded here:

https://github.com/zeffii/Blender_CAD_utils

You can install several ways but the easiest is to [download the zip linked in the readme](https://github.com/zeffii/mesh_tinyCAD/archive/master.zip) and use the Install from File option in _UserPreferences > Addons_. Then you can enable it as usual.

To use it, just select intersecting edges, press W and select TinyCAD > TinyCAD XALL

![tiny cad][1]


  [1]: https://i.sstatic.net/gASae.png