Blender add-on that box selects edges or faces only if their vertices are all within the box.

Installation: Unzip folder. In Blender go to File>User Preferences>Install from File... and chose PickyBoxSelect.py
Search for it in the Add-ons tab and check the check box to activate.

Usage: Search for 'picky box' in the space bar menu or assign a hotkey (e.g. Os-Key+Alt+b) for 'mesh.picky_box_select'. Use like the normal border select. LeftMouse to select, MiddleMouse to deselect, RightMouse to cancel. Undo supported.

Note: With a lot of polygons (>50000-100000) this add-on might get slow.

Todo: Refactoring. Also I am not sure what happens in a mixed mode (e.g. edges & faces).