Hello, hoping someone on here can give me some advice 
We've got an unruly hedge that we inherited from the last owners. It's got a few different plants in it, but one of them is a conifer that's grown far too tall (10 feet) and it's roots are draining the nearby lawn of moisture. We're going to tidy up the rest of the hedge, but want to get rid of this tree. The question is how. We're happy to hire tools etc, but do we simply cut the tree down to a stump and leave it there (I believe the roots will die off but not sure how long that'll take), or try and get the roots out......? We've looked at getting someone in, but we're having other work done so really need to do this ourselves.
Any advice welcome.