Courts have approved and disapproved of the use in jury instructions of a variety of definitions of "proof beyond a reasonable doubt" and "reasonable doubt."

United States v. Taylor, 648 F.2d 565, 570 (9th Cir. 1981) (upholding trial court's admission into evidence of Exhibit 24, which is at best a photocopy of the telecopied January 16, 1975 letter because "Rule 1004(2)....For purposes of the federal best evidence (or original document) rule, an "original" of a writing is the writing itself or any counterpart intended to have the same effect by a person executing or issuing it; the "original" of a recording is is the recording itself or any counterpart intended to have the same effect by a person executing or issuing it; the "original" of a photograph includes the negative or any print taken from the negative; and the "original" of data stored in a computer or similar device includes any printout or other output readable by sight shown to reflect the data accurately.

United States v. Turning Bear, 357 F.3d 730, 733-734 (8th Cir. 2004) (conviction for aggravated sexual abuse of his son and daughter; accused challenged the trial court's exclusion of testimony from a foster care parent who saw the son on a daily basis for four to six months, and that in her opinion, the...Under some circumstances untruthfulness is admissible to impeach a witness.

United States v. Scheffer, 523 U.S. 303, 308 (1998) (accused in general court-martial offered exculpatory polygraph test result; held, Military Rule of Evidence 707 making polygraph inadmissible does not violate....The exclusion of relevant exculpatory evidence offered by a defendant in a trial does not violate a defendant's right to due process or compulsory process or to a defendant's constitutional right to present a defense if exclusion of such exculpatory evidence is not an arbitrary or disproportionate remedy.