I propose a variant versioning scheme that bumps the MINOR version for backwards incompatibilities and reserves MAJOR version bumps for subjectively "big" changes.
This is what the AngularJS versioning scheme was, nearly exactly. Everybody hated it. Hence, semver :)
Huh, thanks for the info! Would you happen to have any hyperlinks to the discussions where people hated on the old scheme? I'd like to read up on this more.