From the legal code of the Creative Commons Attribution 4.0 license (emphasis in the original):
1.a Adapted Material means material subject to Copyright and Similar Rights that is derived from or based upon the Licensed Material and in which the Licensed Material is translated, altered, arranged, transformed, or otherwise modified in a manner requiring permission under the Copyright and Similar Rights held by the Licensor. For purposes of this Public License, where the Licensed Material is a musical work, performance, or sound recording, Adapted Material is always produced where the Licensed Material is synched in timed relation with a moving image.
1.b Adapter's License means the license You apply to Your Copyright and Similar Rights in Your contributions to Adapted Material in accordance with the terms and conditions of this Public License.
1.f Licensed Material means the artistic or literary work, database, or other material to which the Licensor applied this Public License.
2.a Subject to the terms and conditions of this Public License, the Licensor hereby grants You a worldwide, royalty-free, non-sublicensable, non-exclusive, irrevocable license to exercise the Licensed Rights in the Licensed Material to:
2.a.1.A reproduce and Share the Licensed Material, in whole or in part; and
2.a.1.B produce, reproduce, and Share Adapted Material.
2.a.5.B You may not offer or impose any additional or different terms or conditions on, or apply any Effective Technological Measures to, the Licensed Material if doing so restricts exercise of the Licensed Rights by any recipient of the Licensed Material.
3.a.4 If You Share Adapted Material You produce, the Adapter's License You apply must not prevent recipients of the Adapted Material from complying with this Public License.
In short, if the original is CC-BY, you can license derivative works under whatever terms you want, so long as the license of the original work is not infringed by the new terms for the derived work.
In particular, ordinary copyright (aka. "all rights reserved") is a perfectly acceptable copyright for a derivative of a CC-BY work (but the original credits should be included -and augmented- in order to also comply with the original CC-BY).
Also note this doesn't restrict anybody's rights to use the original material under the original license.
The other non-ShareAlike license that permits derivative works (Attribution-Noncommmercial) has a different version of clause 2.a.1.B:
produce, reproduce, and Share Adapted Material for NonCommercial purposes only.
so any license of a derivative work cannot permit commercial use of the original work. It may be possible to permit commercial use of those portions of the derivative that can be separated from the original; this gets into an extreme edge case of copyright law and you'll probably want to consult a lawyer if you find yourself in such a situation.
Another way to consider this issue is by noting that you are only licensing your modifications. For example, if you add a mustache to a CC-BY portrait and use a CC-0 license, only your mustache is CC-0; you can't eliminate the original author's requirement of attribution this way. The derived work would still have to be used under a CC-BY license (or compatible).