If you have CDs and are not interested in converting them to data files and slinging the originals, then you are stuck with at least some of the bulk. In which case I'd suggest a bigger house :-)
You can, of course, take the disks out and get storage "folders" which would allow you to sling the jewel cases. But I suspect that would be an unpopular suggestion.
I can only think that they sit of shelves easily enough, Dedicate a wall of shelves to them so they are in one place, preferably in a room the dogs don't enter, such as your dedicated music room ;-)