Is the Excessive Fines Clause Incorporated Against the States?

From McDonald v. City of Chicago (2010):

We never have decided whether … the Eighth Amendment’s prohibition of excessive fines applies to the States through the Due Process Clause. See Browning-Ferris Industries of Vt., Inc. v. Kelco Disposal, Inc., 492 U. S. 257, 276, n. 22 (1989) (declining to decide whether the excessive-fines protection applies to the States).

But from Cooper Industries, Inc. v. Leatherman Group, Inc. (2001),

[T]he Due Process Clause of the Fourteenth Amendment … makes the Eighth Amendment’s prohibition against excessive fines and cruel and unusual punishments applicable to the States. Furman v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972) (per curiam).

So which is it? Does it matter that Furman spoke only of the Cruel and Usual Punishment Clause of the Eighth Amendment, so that Cooper‘s statement about the excessive fines clause is not backed by any argument or citation?

Commenter Joe noted this two months ago here, but I forgot all about it, and just ran across the issue again today.