What is the preponderance of the evidence standard and what is the clear and convincing evidence standard?

We have previously said that "the preponderance of the evidence standard is a meaningful one that requires the judge to be convinced by a preponderance of the evidence that the fact in question exists." Mezas de Jesus, 217 F.3d at 643 (quotation marks and citation omitted). But, in contrast, the clear and convincing evidence standard is even more demanding and requires that the government "prove [its ] case to a higher probability than is required by the preponderance-of-the-evidence standard." California ex rel. Cooper v. Mitchell Bros.' Santa Ana Theater, 454 U.S. 90, 93 n.6 (1981); see also Black's Law Dictionary 577 (7th ed. 1999) (stating that clear and convincing evidence "indicat[es] that the thing to be proved is highly probable or reasonably certain. This is a greater burden than preponderance of the evidence, .. . but less than evidence beyond a reasonable doubt . . . .").