Appellants Rory and David Doremus were convicted of violating United States Forest Service regulations which prohibit “[djamaging any natural feature or other property of the United States” ( 36 C.F.R. § 261.9 (a) (1987)) and “[vjiolating any term or condition of ... [an] approved operating plan” ( 36 C.F.R. § 261.10 (k) (1987)). On appeal, appellants contend that their activity was permissible as “reasonably incident” to their mining operation (see 30 U.S.C. § 612 (1982)) and that the regulations are unconstitutionally vague. We affirm.

FACTS AND PROCEEDINGS BELOW

Appellants are brothers who have staked mining claims in the Red River Ranger District of the Nez Perce National Forest in central Idaho. Since 1972, appellants have conducted mining operations on these claims under operating plans approved by the Forest Service.

On May 13, 1985, the operating plan at issue was executed by Rory Doremus and Jerry Dombrovske, District Ranger for the Red River Ranger District. Paragraph IV of the plan provides that “[t]he area of exploration will be concentrated to the elear cut,” and that “[n]o more than five trenches will be open at one time.” The magistrate found that the latter provision was proposed by the appellants. The plan also prohibited the cutting of live, green trees for firewood and provided that “[i]f timber is needed operator is asked to cut small dead timber.” The plan neither expressly authorized nor expressly prohibited the removal of live trees in conducting the mining operation.

Between July 23 and July 31, 1985, Forest Service representatives visited the site and observed more than 30 open trenches, some larger than 10 feet by 30 feet, crisscrossing more than lVi acres. Several trees has been pushed over, and a road had been constructed through the trees on one side of the claim. Violation notices were issued, and appellants were tried before a federal magistrate on March 14, 1986. On June 18, 1986, the magistrate issued a memorandum opinion denying the Dore-muses’ motion to dismiss and finding them guilty beyond a reasonable doubt. The Dor remuses appealed to the district court, which affirmed their convictions. United States v. Doremus, 658 F.Supp. 752 (D.Idaho 1987).

STANDARD OF REVIEW

The questions presented involve the construction of federal law and its application to essentially undisputed facts, and therefore they are reviewed de novo. United States v. McConney, 728 F.2d 1195, 1201-02 (9th Cir.) (en banc), cert. denied, 469 U.S. 824 , 105 S.Ct. 101 , 83 L.Ed.2d 46 (1984). The factual findings of the magistrate will not be overturned unless they are clearly erroneous. United States v. Nance, 666 F.2d 353, 356 (9th Cir.), cert. denied, 456 U.S. 918 , 102 S.Ct. 1776 , 72 L.Ed.2d 179 (1982).

DISCUSSION

I. STATUTORY CHALLENGES

A. Applicability of Regulations

Appellants’ first argument is that they are exempted from the prohibitions of 36 C.F.R. Part 261 by the proviso which states:

36 C.F.R. § 261.1 (b) (1987). Appellants contend that their activities were authorized by statute and that therefore the regulations do not prohibit such activities.

Appellants’ statutory rights derive from the provision in the 1872 Act which reserves to the claimant “the exclusive right of possession and enjoyment of all the surface included within the lines of their locations.” 30 U.S.C. § 26 (1982). This right was limited by the Surface Resources and Multiple Use Act of 1955, which reserved to the United States the right to manage and dispose of surface resources on unpat-ented mining claims; however, the 1955 Act provides that such use shall not “endanger or materially interfere with prospecting, mining or processing operations or uses reasonably incident thereto.” 30 U.S.C. § 612 (b) (1982). The same statute also prohibits the removal of vegetative surface resources “[ejxcept to the extent required for the mining claimant’s prospecting, mining or processing operations and uses reasonably incident thereto, ... or to provide clearance for such operations or uses.” 30 U.S.C. § 612 (c).

Appellants argue that the effect of 36 C.F.R. § 261.1 (b) is to exempt mining operations from the general prohibitions of Part 261, thereby limiting the regulation of mining operations to 36 C.F.R. Part 228. We reject this argument. Part 228 does not contain any independent enforcement provisions; it only provides that an operator must be given a notice of noncompliance and an opportunity to correct the problem. 36 C.F.R. § 228.7 (b) (1987). The references to operating plans in § 261.10 would be meaningless unless Part 261 were construed to apply to mining operations, since that is the only conduct for which operating plans are required under Part 228. In addition, 16 U.S.C. § 478 (1982), which authorizes entry into national forests for “all proper and lawful purposes, including that of prospecting, locating, and developing the mineral resources thereof,” specifically states that “[sjuch persons must comply with the rules and regulations covering such national forests.” This statutory caveat encompasses all rules and regulations, not just those (such as Part 228) which apply exclusively to mining claimants. In this context, § 261.1(b) is merely a recognition that mining operations “may not be prohibited nor so unreasonably circumscribed as to amount to a prohibition.” United States v. Weiss, 642 F.2d 296, 299 (9th Cir.1981).

B. Validity of Regulations

Next, appellants argue that even if Part 261 applies to them, the Forest Service is barred by 30 U.S.C. § 612 from prohibiting any conduct unless it proves that the conduct was not “reasonably incident” to their mining operation. The district court rejected this argument, holding that “the operating plan itself becomes the definition of what is reasonable and significant conduct under the circumstances,” and that therefore any violation of the operating plan was per se unreasonable under the statute. 658 F.Supp. at 755 . The district court also held that the regulations did not conflict with 30 U.S.C. § 612 because “th[e] regulatory right is limited so as not to endanger or materially interfere with mining operations.” Id. at 756 , citing United States v. Richardson, 599 F.2d 290 (9th Cir.1979), cert. denied, 444 U.S. 1014 , 100 S.Ct. 663 , 62 L.Ed.2d 643 (1980).

We agree with the district court that 36 C.F.R. § 261.10 (k) is consistent with the mining laws. The regulatory scheme of requiring a notice of intent to operate and approval of an operating plan is a reasonable method of administering the statutory balance between “the important interests involved here [which] were intended to and can coexist.” Weiss, 642 F.2d at 299 . The purpose of requiring prior approval is to resolve disputes concerning the statutory balance before operations are begun, not after. If the appellants were unsatisfied with the conditions of the plan, they could have appealed to the Regional Forester under 36 C.F.R. § 228.14 (1987). His decision would then be subject to review under the Administrative Procedure Act. See 5 U.S.C. §§ 701 et seq. (1982); cf. Sabin v. Butz, 515 F.2d 1061, 1065 (10th Cir.1975) (recognizing jurisdiction under APA to review denial of special use permit). David Doremus admitted in his opening brief that appellants recognized that an appeal was a possible course of action and deliberately chose to forego it. David Doremus’ Opening Brief at 23. Having failed to appeal the plan, appellants may not now complain that the restriction limiting appellants to five open trenches was “unreasonable.” See United States v. Brunskill, 792 F.2d 938, 941 (9th Cir.1986) (refusing to consider merits of operating plan where defendants did not appeal rejection of proposed plan); cf. United States v. Curtis-Nevada Mines, Inc., 611 F.2d 1277, 1286 (9th Cir.1980) (enjoining claimant from prohibiting public recreational use on his claim; noting that claimant could protest to federal agency and, if unsatisfied, bring lawsuit).

We also agree that 36 C.F.R. § 261.9 (a) does not conflict with the mining laws. This provision is subject to § 261.1(b), which incorporates appellants’ statutory rights under 30 U.S.C. § 612 . However, although appellants have a right to dispose of vegetative resources where such disposal is “reasonably incident” to their mining operation, they may not exercise that right without first obtaining approval of their operation in the manner specified in 36 C.F.R. Part 228. If appellants believed that their operation required the removal of trees and that the plan failed to accomo-date that need, their remedy was to appeal the plan prior to commencing operations. Appellants may not blithely ignore Forest Service regulations and argue afterward that their conduct was “reasonable.”

Appellants argue, however, that Richardson holds that the government must show that their conduct was unreasonable in order to prohibit it. We disagree. In Richardson , the government filed a civil action to enjoin the Richardsons from blasting and bulldozing on their mining claims and to require restoration of the surface. The court specifically noted that although “the Secretary of Agriculture has ... authority under sections 478 and 551 of Title 16 to promulgate regulations concerning the methods of prospecting and mining in national forests; ... [n]o such regulations were in effect before this lawsuit was commenced.” 599 F.2d at 292 . In the absence of any regulatory guidance, the court looked directly to 30 U.S.C. § 612 to determine whether the Richardsons’ activities were “reasonably incident” to their mining operation. Thus, Richardson held that the Forest Service could enjoin unreasonable mining operations even in the absence of specific regulations. Richardson did not hold that the Service could not enforce a reasonable regulatory scheme requiring mining operators to receive prior approval before beginning work.

We conclude that the requirement of pri- or approval does not “endanger or materially interfere with” appellants’ mining operations, and that the regulations at issue are therefore consistent with 30 U.S.C. § 612 .

II. CONSTITUTIONAL CHALLENGE

A statute is void for vagueness if it fails to give adequate notice to people of ordinary intelligence concerning the conduct it proscribes, or if it invites arbitrary and discriminatory enforcement. Schwartzmiller v. Gardner, 752 F.2d 1341, 1345 (9th Cir.1984). “The threshold question in any vagueness challenge is whether to scrutinize the statute for intolerable vagueness on its face or whether to do so only as the statute is applied in the particular case.” Id. at 1346 .

Where the statute or regulation does not implicate constitutionally protected conduct, a facial challenge will succeed “only if the enactment is impermissibly vague in all of its applications.” Village of Hoffman Estates v. The Flipside, Hoffman Estates, Inc., 455 U.S. 489, 494-95 , 102 S.Ct. 1186, 1191 , 71 L.Ed.2d 362 (1982). In such a case, “[a] plaintiff who engages in some conduct which is clearly proscribed cannot complain of the vagueness of the law as applied to the conduct of others. A court should therefore examine the complainant’s conduct before analyzing other hypothetical applications of the law.” Id. at 495 , 102 S.Ct. at 1191 , see also id. at 500, 102 S.Ct. at 1194 (“Flipside’s facial challenge fails because ... the ordinance is sufficiently clear as applied to Flipside.”) (emphasis added).

In this case, it is clear that no constitutionally protected conduct is implicated, nor is the statute so vague as to specify “no standard of conduct at all.” See United States v. Westbrook, 817 F.2d 529, 531-32 (9th Cir.1987); Schwartzmiller, 752 F.2d at 1348 . Therefore, we need only consider whether the regulations are vague as applied. United States v. Hogue, 752 F.2d 1503, 1504 (9th Cir.1985).

A. 36 C.F.R. § 261.10 (h)

This regulation prohibits “[violating any term or condition of a special-use authorization, contract or approved operating plan.” Appellants’ claim that the operating plan is ambiguous is without merit. Paragraph IV-A of the plan provides:

The meaning of this provision is crystal clear. The plan, which covers all operations pertaining to six listed claims, imposes an overall limit of five open trenches for the entire area of exploration. It also allows one open discovery pit (not counted as a trench) for each of the six claims. The provision is not only not vague, it is defined with numerical precision. No reasonable person could construe the plan as allowing more than thirty trenches open simultaneously.

Again, however, appellants rely on 36 C.F.R. § 261.1 (b), which states that “[njothing in this part shall preclude activities as authorized by ... the U.S. Mining Laws Act of 1872 as amended.” Their contention is that a reasonable person of ordinary intelligence would have believed that he could exceed the operating plan so long as his work was “reasonably incident” to his mining claim. Appellants also rely on 36 C.F.R. § 228.7 , which states that a notice of non-compliance will be issued “[i]f an operator fails to comply with ... his approved plan of operations and the noncompliance is unnecessarily or unreasonably causing injury, loss or damage to surface resources” (emphasis added). From this, appellants argue that the regulations contemplate conduct which is not in compliance with the operating plan but which is also not unnecessary or unreasonable.

In Hoffman Estates, the Supreme Court listed a number of factors which affect the degree of vagueness which the Constitution tolerates. 455 U.S. at 498-99 , 102 S.Ct. at 1193 . First, economic regulation is subject to a less strict vagueness test, because its subject matter is often more narrow and because businesses can be expected to consult relevant legislation in advance of action. The court added that “the regulated enterprise may have the ability to clarify the meaning of the regulation by its own inquiry, or by resort to an administrative process.” Id. at 498 , 102 S.Ct. at 1193 . Second, a stricter vagueness test applies where criminal penalties are involved. Indeed, although the licensing regulation in Hoffman only imposed civil penalties, the court treated it as “quasi-criminal” because of its prohibitory and stigmatizing effect. Id. at 499-500 & n. 16, 102 S.Ct. at 1194 n. 16. Third, a scienter requirement may mitigate vagueness, especially with respect to the adequacy of notice to the complainant. Fourth, a more stringent test is applied when the law threatens to inhibit the exercise of constitutionally protected rights.

Analyzing § 261.10(k) in light of these factors, we conclude that it is not unconstitutionally vague. Although the regulation imposes criminal penalties, in effect it acts as an economic regulation governing the conduct of mining operations on National Forest lands. As with an economic regulation, the subject matter is narrow, and mining operators are not only expected, but required, to obtain advance approval. Thus, the Doremuses had “the ability to clarify the meaning of the regulation by [their] own inquiry, or by resort to the administrative process.” Hoffman Estates, 455 U.S. at 498 , 102 S.Ct. at 1193 , cf. Joseph E. Seagram & Sons, Inc. v. Hostetter, 384 U.S. 35, 49 , 86 S.Ct. 1254, 1263 , 16 L.Ed.2d 336 (1966) (“we think it plain under our decisions that ... the limits of administrative action are sufficiently definite or ascertainable so as to survive challenge on the grounds of unconstitutionality.”). This ability greatly mitigates the strict liability nature of the offense. Finally, no constitutionally protected rights are implicated in this case. We therefore hold that § 261.10(k) is not unconstitutionally vague as applied.

B. 36 C.F.R. § 261.9(a)

This regulation prohibits “[djamaging any natural feature or other property of the United States.” “Damaging” is defined as “to injure, mutilate, deface, destroy, cut, chop, girdle, dig, excavate, kill or in any way harm or disturb.” 36 C.F.R. § 261.2 .

Appellants argue that the definition of “damaging” invites arbitrary and discriminatory enforcement because any entry into a national forest will “disturb” some natural feature. For the reasons outlined above, we decline to address this “facial” argument. As stated by the district court, “[cjertainly, damage is inflicted when a live tree is destroyed by being pushed over.” 658 F.Supp. at 758 .

The district court found it equally clear that “live green trees are a feature of nature.” Id. We agree. Appellants argue, however, that the district court failed to consider the effect of a companion regulation, 36 C.F.R. § 261.6 (a), which prohibits “[cjutting or otherwise damaging any timber, tree or other forest product, except as authorized by a special use authorization, timber sale contract, or Federal law or regulation” (emphasis added). We see no inconsistency. § 261.6(a) merely makes explicit the proviso in § 261.1(b), which excepts all activity authorized by Federal law. The flaw in appellant’s argument is that 30 U.S.C. § 612 does not authorize mining operators to act without Forest Service approval, and the operating plan did not authorize the cutting of live trees. The plan addresses only small amounts of timber needed for the mining operation; it does not give appellants a blanket license to remove live trees in any manner and quantity which they believe to be reasonable. We therefore conclude that § 261.9(a) is not unconstitutionally vague as applied.

III. CONCLUSION

In summary, we hold that the regulations at issue are consistent with the statutory scheme and are not unconstitutionally vague. Appellants’ convictions are therefore

AFFIRMED.

. According to the testimony of a Forest Service officer, at least one of the trenches was dug after appellants were issued a notice of noncompliance and ordered to shut down on July 26. . David Doremus also contends that appellants attempted on several occasions to appeal Forest Service decisions concerning their plan. The record shows only that appellants sent two letters of complaint to Ron Gardner, a Forest Service official. One of the letters (dated January 18, 1985) was sent prior to the violations complained of, and although the subsequent letter characterized the January 18 letter as an "appeal" and "demanded” that it be processed, nothing in the original letter indicated that it constituted an appeal, and the Forest Service did not treat it as one. If appellants were dissatisfied with the Forest Service’s response, they could have filed an action to compel the Service to process the appeal. See 5 U.S.C. § 706 (1) (1982). . Appellants other claims are wholly without merit. First, the magistrate’s finding that no oral amendments to the plan were made in 1985, except for an authorization to remove one tree, is not clearly erroneous. Second, the Forest Service Manual merely establishes guidelines for the exercise of the Service's prosecuto-rial discretion; it does not act as a binding limitation on the Service’s authority. Finally, neither the jury trial nor the separation of powers issues were raised below, and we will not consider them for the first time on appeal. Scott v. Pacific Maritime Ass’n, 695 F.2d 1199, 1203 (9th Cir.1983). . Appellants also contend that the regulation invites arbitrary and discriminatory enforcement because "[t]he prohibited conduct is defined only in the operating plan, which may be unilaterally imposed upon Defendants by the district ranger.” Rory Doremus’ Opening Brief at 43. We reject this contention. The conditions of the operating plan are subject to negotiation, and the claimant may appeal any decision regarding the plan to the Regional Forester and, if necessary, seek judicial review. The amici contend that the regulations are invalid under Yick Wo v. Hopkins, 118 U.S. 356 , 6 S.Ct. 1064 , 30 L.Ed. 220 (1886). It is true that the Court in Yick Wo strongly suggested that the ordinances involved there were invalid on their face because they conferred unrestrained discretion to deny a permit. 118 U.S. at 366 , 6 S.Ct. at 1068-69 . However, the Court explicitly chose not to rely on this ground, relying instead on the fact that the ordinance was discriminatorily applied on the basis of race. Id. at 373-74 , 6 S.Ct. at 1072-73 . There is no suggestion that such is the case here.