Setting to make [incremental|full] backup and nightly clean-up mutualy exclusive

The backup of one of our servers takes the better part of the day (which isn’t much of a problem in itself), the clean-up is set to “1-7/0-24” as we don’t care when it runs.

Would it be possible to get a setting to make the clean-up wait till all backups have finished and make any new backups wait till the clean-up has finished to ease on the disk contention?