PER CURIAM:

Defendant-appellant Frederick G. Delibac appeals from a judgment entered in the United States District Court for the District of Vermont (Franklin S. Billings, Chief Judge), convicting defendant of various violations of the federal narcotics laws and of using and carrying a firearm during and in relation to the narcotics offenses. On appeal, we consider Delibac's challenges to the district court's (1) admission of evidence pursuant to the "plain view" doctrine; (2) charge to the jury on the definition of reasonable doubt; and (3) rejection of his argument that the United States Sentencing Guidelines (the "Guidelines") offend due process because they accord undue authority to prosecutors. Since we find that the district court committed no error, we affirm.

BACKGROUND

On the night of April 27, 1989, the Vermont State Police were in the midst of an investigation of cocaine trafficking by one Edmund Brooks. Vermont State Police Detective Sergeant Leo Blais, acting in an undercover capacity, arranged for the purchase of two ounces of cocaine from Brooks. Brooks and Detective Roger Marcoux, also acting undercover, later met at a shopping center. After a series of events not germane to our discussion, Brooks agreed to sell Detective Marcoux the two ounces of cocaine. Before Brooks was paid for the transaction, he was placed under arrest. A search of Brooks' person revealed a voice-activated paging device, which sounded several times while Brooks was being booked. The arresting officers determined that the telephone numbers left on the pager were subscribed to by Delibac and a paging company that leased the pager to Brooks' employer, Fort Construction Company, an entity owned by Delibac.

Detective Marcoux telephoned Delibac and offered to pay him $1,700 for one of the two ounces of cocaine that Brooks had earlier supplied. In response to a question posed by Detective Marcoux, Delibac stated that Detective Marcoux should not be fearful of meeting Delibac "as long as everything goes alright." The two agreed to meet at a parking lot.

The meeting that ensued in the parking lot, which was recorded and played for the jury, was held in Delibac's automobile. Delibac acknowledged that he had supplied the cocaine furnished by Brooks, accepted the $1,700 from Detective Marcoux, and placed it in the car ashtray. During a conversation concerning future drug transactions, Delibac admitted that he had a gun with him. Detective Marcoux then persuaded Delibac to show him Delibac's "stash." Just before the two left the parking lot, Delibac admitted that he also had a gun located at the "stash."

The "stash," as it turned out, was Delibac's office at the Fort Construction Company. In the office, Delibac displayed five ounces of cocaine to Detective Marcoux. Detective Marcoux agreed to buy the additional cocaine for $1,450 per ounce the next day. Upon exiting the building, Delibac was placed under arrest.

Detective Marcoux immediately recovered the $1,700 from Delibac's car ashtray and then gave Delibac Miranda warnings. Delibac stated his willingness to consent to a search of his office, provided the officers did not "trash" his office and take his personal papers. Detective Blais, who had been monitoring the recorded conversation and had just arrived on the scene, produced a consent-to-search form. Delibac's consent, as reflected on the executed form, was limited to a search of his office and car and seizure of the five ounces of cocaine in the office. A search of Delibac's car uncovered a Smith Wesson Model .357 Magnum (the "Magnum") located between the driver's bucket seat and the console.

Detective Marcoux, assisted by other officers including Detective Blais, searched Delibac's office and seized the five ounces of cocaine. One of the other officers, however, opened a file cabinet drawer and discovered $39,000 in cash. Delibac, who was seated outside his office with Detective Douglas Reisden, told Detective Reisden that more drugs could be found in a desk drawer and that the officers "might as well have all of it." Detective Reisden relayed this information to the officers conducting the search. The officers found a quantity of marijuana and eleven additional individually wrapped packages of cocaine in the desk. As Detective Blais walked around the desk, he saw a partially hidden .9 mm. Walther pistol (the "Walther"), located on a cabinet shelf and seized it.

After the search, Delibac was taken to Colchester State Police Barracks where, after being re-advised of his constitutional rights, he admitted that he had recently obtained nine ounces of cocaine from an individual in New York City.

Delibac was charged in a seven-count indictment with conspiring with others to distribute cocaine and to possess with intent to distribute cocaine, in violation of 21 U.S.C. § 846 (Count 1); knowingly and intentionally distributing cocaine, in violation of 21 U.S.C. § 841(a)(1) (Counts 2, 3, and 4); possession with intent to distribute cocaine, in violation of 21 U.S.C. § 841(a)(1) (Count 5); using and carrying a firearm during and in relation to a drug trafficking crime, in violation of 18 U.S.C. § 924(c) (Count 6); and using a firearm during a drug trafficking crime, in violation of 18 U.S.C. § 924(c) (Count 7).

Following a hearing, the district court granted Delibac's motion to suppress the $39,000 in cash, the eleven additional packages of cocaine and the marijuana, but denied Delibac's motion to suppress his oral statements, the firearms and the $1,700 in cash recovered from the car ashtray. Delibac conceded that he voluntarily consented to the seizure of the five ounces of cocaine displayed to Detective Marcoux. The district court found that Delibac's oral consent given to Detective Reisden, which was considerably broader than the written consent reflected on the consent-to-search form, was obtained as a result of "presumptive coercion." As to the firearms, the district court found that the Magnum was properly obtained under the "automobile exception" to the warrant requirement and that the Walther was properly seized under the plain view doctrine.

The government's subsequent motion to dismiss Counts 2 and 3 of the indictment was granted and the case proceeded to a two-day jury trial. On November 14, 1989, the jury returned a guilty verdict on Counts 1, 4, 5, and 6 and acquitted Delibac on Count 7, which charged him with using the Walther during and in relation to the possession count charged in Count 5. Delibac was sentenced to concurrent terms of 51 months on Counts 1, 4, and 5, and a consecutive 60-month term, as mandated by statute, on Count 6. In addition to the 111-month prison term, the district court imposed a three-year term of supervised release, a $10,000 fine and a mandatory $200 special assessment.

Delibac's appeal raises numerous issues, only three of which merit discussion. First, Delibac challenges the district court's conclusion that the "plain view" doctrine permitted the admission of the Walther at trial; he argues that the officers, particularly Detective Blais, were not lawfully in Delibac's office when the Walther was observed. Second, Delibac alleges that he was denied a fair trial because the district court incorrectly defined reasonable doubt to the jury. Finally, Delibac claims that the Guidelines unconstitutionally vest prosecutors with the power to sentence.

DISCUSSION

I. THE PLAIN VIEW DOCTRINE

In United States v. Barrios-Moriera, 872 F.2d 12 (2d Cir. 1989), cert. denied, ___ U.S. ___, 110 S.Ct. 364, 107 L.Ed.2d 350 (1990), we set forth the requirements for invoking the "plain view" doctrine. "First, the initial intrusion by the police officer must be lawful so that he can justify being in a position to make his discovery . . . . Second, the discovery must be inadvertent. . . . Third, the police must have had probable cause to believe that the item seized was evidence of a crime." Id. at 16 (citations omitted). The Supreme Court has since rejected the inadvertence requirement. See Horton v. California, ___ U.S. ___, 110 S.Ct. 2301, 2309, 110 L.Ed.2d 112 (1990).

Of the two remaining criteria, only the first concerns us here. Delibac claims that when the Walther was spotted, the officers were no longer legitimately in his office because they had completed their search pursuant to his invalid oral consent.

The officers were initially on the premises pursuant to Delibac's valid written consent. When they remained on the premises and continued to search after Delibac's oral consent, which was later determined invalid, it is clear that the officers still "entertained a good faith belief that consent had been obtained." United States v. Diaz, 577 F.2d 821, 824 (2d Cir. 1978) (Friendly, J.). The fact that it was Detective Blais who both monitored the recorded conversation in Delibac's car and negotiated the terms of the written consent does not alter this conclusion. Detective Blais was dealing with an otherwise cooperative suspect during a valid consensual search and was advised by Detective Reisden that Delibac had just orally agreed to expand the scope of that search. It was objectively reasonable for Detective Blais to believe that he was lawfully on the premises when the Walther was found. We conclude, therefore, that the seizure of the Walther properly falls within the "plain view" doctrine.

II. THE REASONABLE DOUBT CHARGE

Delibac also attacks the district court's reasonable doubt charge. Significantly, however, no objection to the charge was made at trial. Accordingly, our review is limited by the plain error standard of Fed.R.Crim.P. 52(b). See United States v. Frady, 456 U.S. 152, 163, 102 S.Ct. 1584, 1592, 71 L.Ed.2d 816 (1982). The district court instructed the jury as follows:

In a criminal case the government has the burden of proving each element of the charges against the defendant beyond a reasonable doubt. You cannot find the defendant guilty unless the government has met this burden of proof.

To support a verdict of guilty, you need not find every fact beyond a reasonable doubt. You need only find that the government has established by the evidence and beyond a reasonable doubt each and every essential element of the crime charged.

A reasonable doubt is a fair doubt, based upon the application of reason and common sense to the evidence presented. The law does not require proof that overcomes all possible doubt, so a reasonable doubt means only a substantial doubt. Similarly, beyond a reasonable doubt does not mean no doubt.

A reasonable doubt may arise from — may arise either from the evidence presented or from the lack of evidence presented.

Once again, a district court has failed to heed our repeated warnings against embellishing upon the standard instruction recommended in 1 Devitt Blackmar, Federal Jury Practice and Instructions § 11.14 (3d ed. 1977). See United States v. Gatzonis, 805 F.2d 72, 74 (2d Cir. 1986), cert. denied, 484 U.S. 932, 108 S.Ct. 303, 98 L.Ed.2d 262 (1987); United States v. Viafara-Rodriguez, 729 F.2d 912, 913-14 (2d Cir. 1984); United States v. Ivic, 700 F.2d 51, 69 (2d Cir. 1983). Here, the paraphrase creates three problems. First, the charge failed to instruct the jurors that proof beyond a reasonable doubt is "proof of such a convincing character that a reasonable person would not hesitate to rely and act upon it in the most important of his own affairs." Second, the charge equated "reasonable" doubt with "substantial" doubt — an unenlightening instruction that we have only "tolerated." See Ivic, 700 F.2d at 69 n. 12. Finally, the charge advised the jury that "to support a verdict of guilty, you need not find every fact beyond a reasonable doubt." While we have noted that, as an abstract proposition, this instruction is a correct statement of the law, we have also advised that in an instruction to a jury it is probably confusing and certainly unnecessary. See Gatzonis, 805 F.2d at 74; Viafara-Rodriguez, 729 F.2d at 913.

Although we find it necessary to "state our views on this issue" again, Gatzonis, 805 F.2d at 74, we are nevertheless satisfied that the charge taken as a whole, Cupp v. Naughten, 414 U.S. 141, 146-47, 94 S.Ct. 396, 400-01, 38 L.Ed.2d 368 (1973), adequately conveys the concept of reasonable doubt and does not constitute plain error. See Henderson v. Kibbe, 431 U.S. 145, 154, 97 S.Ct. 1730, 1736, 52 L.Ed.2d 203 (1977).

III. SENTENCING GUIDELINES

Delibac also mounts a due process challenge to the Guidelines. He notes that prosecutors are empowered to decide which criminal statutes to enforce. Once the charges are made and a conviction is obtained, the district court then has limited discretion at sentencing. Therefore, the argument goes, the Guidelines improperly vest the prosecutor with the power to manipulate the sentence.

We reject this argument. That a particular penalty may be a factor in the prosecutor's charging calculus is not, in and of itself, a due process violation. See United States v. Batchelder, 442 U.S. 114, 124-25, 99 S.Ct. 2198, 2204-05, 60 L.Ed.2d 755 (1979); see also United States v. Pick, 724 F.2d 297, 301 (2d Cir. 1983) ("a decision to prosecute under the statute with the heavier penalty `does not empower the Government to predetermine ultimate criminal sanctions'") (quoting Batchelder, 442 U.S. at 125, 99 S.Ct. at 2205). In addition, there exists no procedural due process right to an individualized sentence, and to the judicial discretion that it accords, in a noncapital crime. See United States v. Vizcaino, 870 F.2d 52, 56 (2d Cir. 1989); cf. United States v. Huerta, 878 F.2d 89, 93-94 (2d Cir. 1989) (rejecting, on the authority of Vizcaino, a due process challenge to substantial assistance motions under 18 U.S.C. § 3553(e) on the ground that it vests prosecutors with unlimited and unreviewable discretion), cert. denied, ___ U.S. ___, 110 S.Ct. 845, 107 L.Ed.2d 839 (1990). Thus, in the absence of a bona fide charge that the prosecutor was motivated by bad faith or discrimination — and no such charge is made here — we conclude that the Guidelines do not vest undue sentencing authority to prosecutors in violation of the Due Process Clause. Accord United States v. Thomas, 884 F.2d 540, 544 (10th Cir. 1989).

We have considered Delibac's remaining contentions and find them to be without merit. Accordingly, we affirm the judgment of the district court.