It may seem backwards to suggest that good writing amounts mostly to writing with the bad stuff subtracted; but in my experience the inverse idea - that good writing amounts mostly to writing with good stuff added - leads to an overreliance on tricks and contrivances, i.e. preciousness.
There's maybe one writer in a thousand with the talent to succeed at preciousness. (Margaret Atwood comes to mind; I tend to read her books with a dictionary close at hand.) For the rest of us, the straightest path to good writing is to stop trying so hard and just aim for good structure, clarity and brevity.
That means you need to develop a thick skin, by which I mean a willingness to let go of the stuff that doesn't work. Few contemporary critics would regard Stephen King as a literary giant, but he clearly knows how to get the words onto the paper and into the hands of readers. His most salient writing advice? "Kill your darlings."