Deep revision for me often means cutting characters, adding characters, changing plot points, strengthening desire lines, and once *gasp* changing the premise, which meant rewriting that entire novel. Deep revision also includes cutting chapters and writing new chapters and scenes.
Below are links to other authors who share their revision process. All their examples are excellent.
Janni Simner posted various versions and an excellent analysis of the opening paragraphs of her short story, "Song for Two Voices" in 2005. In this post she also talks about finding the right voice for this story. She often shares thoughts about revision on her blog.
Sarah has an MFA in Writing for Children and Young Adults from Vermont College of Fine Arts. She is a writer and photographer whose blog explores writing craft, stories and the cultures (and places) she lives.
She has lived in Brazil, Finland, Iceland, China, Germany, Nigeria, and many places in the United States. Currently, she lives in Egypt. Her website is at http://www.sarahblakejohnson.com/