Well, first you need the T-shirt. I remember it from my last science-fiction convention, about twenty years ago. It reads:

I AM A BOOKAHOLIC.
IF YOU ARE A DECENT PERSON,
YOU WILL NOT SELL ME ANY MORE BOOKS.

Then you could set up a transitional plan about carrying out two books for each one you bring in.
But I'd go with the shelves, on general principles. ;D

A few months ago I invited an antiquarian bookseller into my basement, and he took out several dozens of cases as a job lot. Part of it was finally admitting that if I hadn't yet read some of them, I likely would never do so. There's a lot to be said for sending them away to a good home where they'll be loved and looked after. And empty shelves can be a glorious sight. ;D