Opinion for the Court filed by Circuit Judge RANDOLPH.
Concurring opinion filed by Senior Circuit Judge EDWARDS.
RANDOLPH, Circuit Judge.
The United States and other countries entered into the Montreal Protocol on Substances that Deplete the Ozone Layer, Sept. 16, 1987, S. Treaty Doc. NO. 100-10, [225]*2251522 U.N.T.S. 29 (“Montreal Protocol”), a treaty in which the signatory nations agreed to reduce the use of certain substances, including methyl bromide, that degrade the stratospheric ozone layer. The Environmental Protection Agency issued a rule implementing “critical use” exemptions from the treaty’s general ban on production and consumption of methyl bromide. Protection of Stratospheric Ozone: Process for Exempting Critical Uses From the Phaseout of Methyl Bromide, 69 Fed. Reg. 76,982 (Dec. 23, 2004) (codified at 40 C.F.R. pt. 82) (“Final Rule”). We dismissed the Natural Resources Defense Council’s petition for judicial review for lack of standing. Natural Res. Def. Council v. EPA, 440 F.3d 476, 477-78 (D.C.Cir. 2006) (“NRDC I”). In their respective petition for and opposition to rehearing, NRDC and EPA offered new information that has led us to change our view of the standing issue. We therefore grant the petition for rehearing, withdraw our previous opinion, and decide the merits. Fed. R. App. P. 40(a)(4)(A); see, e.g., Moldea v. New York Times Co., 22 F.3d 310, 311-12 (D.C.Cir.1994).
I.
In the mid-1970s, scientists discovered that certain man-made chemicals can destroy the layer of ozone gas in the stratosphere approximately ten to twenty-five miles above the Earth’s surface. Stratospheric ozone absorbs ultraviolet radiation; as the ozone layer thins, less radiation is absorbed. Increased human exposure to ultraviolet radiation is linked to a range of ailments, including skin cancer and cataracts.
Amidst growing international concern about ozone depletion, the United States and twenty-four other nations entered into the Montreal Protocol. The Protocol requires signatory nations — which now number 189 — to reduce and eliminate their production and use of ozone-depleting chemicals in accordance with agreed-upon timetables. Montreal Protocol arts. 2-21. The Senate ratified the treaty in 1988, and Congress incorporated its terms into domestic law through the Clean Air Act Amendments of 1990, Pub.L. No. 101-549, tit. VI, 104 Stat. 2399, 2648. Since then, the United States has reduced its use of methyl bromide to less than 39% of its 1991 baseline.
In 1997, the Parties “adjusted” the Protocol to require developed-country Parties to cease “production” and “consumption” 1 of methyl bromide by 2005. See Montreal Protocol art. 2H(5).2 In response, Congress amended the Clean Air Act to require EPA to “promulgate rules for reductions in, and terminate the production, importation, and consumption of, methyl bromide under a schedule that is in accordance with, but not more stringent than, the phaseout schedule of the Montreal [226]*226Protocol Treaty as in effect on October 21, 1998.” 42 U.S.C. § 7671c(h).
Methyl bromide is a naturally occurring gas produced by oceans, grass and forest fires, and volcanoes. U.S. Dep’t of Agrie., Agrie. Research Serv., Soil Physics & Pesticide Research: Methyl Bromide 1 (2005), http://www.ars.usda.gov/Research/ docs.htm?docid=10408. It is also man-made and used as a broad-spectrum pesticide. See Final Rule, 69 Fed.Reg. at 76,-983. Methyl bromide is typically injected into soil as a fumigant before several types of crops are planted. The United States regulates methyl bromide as a “class I” ozone-depleting substance. See 42 U.S.C. § 7671c(h). Methyl bromide has an “ozone depletion potential” (“ODP”) of 0.38-0.60. This puts it in the middle range of substances scheduled for elimination under the Protocol. It is not nearly as destructive as chlorofluoroearbons and most other class I substances, almost all of which were phased out in 2000. 42 U.S.C. § 7671e(b). On the other hand, it is significantly more destructive than “class II” substances, which are to be phased out in 2030. See 42 U.S.C. § 7671d(b).
In light of methyl bromide’s wide use and the lack of comparable substitute pesticides, see Final Rule, 69 Fed.Reg. at 76,985, the Protocol allows exemptions from the general ban “to the extent that the Parties decide to permit the level of production or consumption that is necessary to satisfy uses agreed by them to be critical uses.” Montreal Protocol art. 2H(5); see also 42 U.S.C. § 7671c(d)(6) (“To the extent consistent with the Montreal Protocol, the [EPA] Administrator ... may exempt the production, importation, and consumption of methyl bromide for critical uses.”). The Parties to the Protocol meet annually to “decide to permit the level of production or consumption that is necessary to satisfy uses agreed by them to be critical uses.” Montreal Protocol art. 2H(5). At one of these meetings the Parties set general guidelines for implementing the critical-use exemptions, see Ninth Report, supra note 2, at 26-27 (“Decision IX/6”), and at another the Parties approved exemptions for 2005. The United States formally began the process of establishing its 2005 critical-use exemptions in May 2002, when EPA published a notice in the Federal Register seeking applications for 2005 and 2006 critical uses of methyl bromide and the amounts of new production and consumption needed to satisfy those uses. See Protection of Stratospheric Ozone: Process for Exempting Critical Uses From the Phaseout of Methyl Bromide, 67 Fed.Reg. 31,798 (May 10, 2002). EPA teams composed of biologists and economists reviewed each application and decided which to include in the aggregate U.S. nomination to the Parties. The final U.S. nomination, submitted to the Montreal Protocol’s administrative body (the “Ozone Secretariat”) in February 2003, requested a total exemption of about ten-thousand metric tons of methyl bromide for sixteen different uses.
The process then moved to the international stage. Two working groups operating under the auspices of the Ozone Secretariat — the “Methyl Bromide Technical Options Committee” and the “Technology and Economic Assessment Panel” — evaluated each country’s nomination and made a recommendation to the Parties at their November 2003 meeting. At that meeting, the Parties deadlocked over the proposed critical-use exemptions and called an “extraordinary meeting” to make the final decisions. See U.N. Env’t Programme, Report of the Fifteenth Meeting of the Parties to the Montreal Protocol on Substances that Deplete the Ozone Layer, U.N. Doc. UNEP/OzL.Pro.15/9, at 8-11, 77-78 (Nov. 11, 2003).
[227]*227The Parties reached agreement at their First Extraordinary Meeting in March 2004. They granted the United States critical uses in sixteen categories, amounting to 8,942 metric tons of methyl bromide. To satisfy these critical uses, the Parties authorized 7,659 metric tons of new production and consumption, with the remainder (1,283 metric tons) to be made up from existing stocks of methyl bromide. See U.N. Env’t Programme, Report of the First Extraordinary Meeting of the Parties to the Montreal Protocol on Substances that Deplete the Ozone Layer; U.N. Doc. UNEP/OzL.Pro.ExMP/1/3, at 14-15, 26 (Mar. 27, 2004) (“Decision Ex.I/ 3”). Decision Ex.I/3 noted that “each Party which has an agreed critical use should ensure that the criteria in paragraph 1 of decision IX/6[3] are applied when ... authorizing the use of methyl bromide and that such procedures take into account available stocks.” Id. ¶ 5.
With Decision Ex.I/3 in hand, EPA proposed rules to implement the critical-use exemption. See Protection of Stratospheric Ozone: Process for Exempting Critical Uses From the Phaseout of Methyl Bromide, 69 Fed.Reg. 52,366 (Aug. 25, 2004). Many parties, including NRDC, submitted comments. The Final Rule, issued in December 2004, authorized new production and consumption up to the limit established in Decision Ex.I/3. Final Rule, 69 Fed.Reg. at 76,990 tbl.l. It also authorized the use of stocks as permitted by the decision, id. at 76,986, 76,991 tbl.2, and permitted noncritical users to draw upon existing stocks, id. at 76,988.4
NRDC believes the Final Rule violated Decision IX/6 and Decision Ex.I/3 because EPA failed to disclose the full amount of existing stocks, failed to offset new production and consumption by the full amount of these stocks, and failed to reserve the stocks for critical uses, and because the total amount of methyl bromide critical use the Final Rule authorized is not the technically and economically feasible minimum.5 These claims depend upon the legal status of Decisions IX/6 and Ex.I/3.
After oral argument, we ordered supplemental briefing to address the question whether consensus decisions of the Parties are “cognizable in federal court actions brought to enforce the Protocol and the relevant terms of the Clean Air Act.” EPA and NRDC agree that the decisions are not “adjustments” to the Protocol. But they disagree on the legal consequences of the decisions.
II.
In order for this court to have Article III jurisdiction, NRDC had to establish that at least one of its members has standing to sue in his own right, the inter-[228]*228ests the association seeks to protect are germane to its purpose, and individual members need not participate in the lawsuit themselves. Sierra Club v. EPA, 292 F.3d 895, 898 (D.C.Cir.2002) (citing Hunt v. Wash. State Apple Adver. Comm’n, 432 U.S. 333, 342-43, 97 S.Ct. 2434, 53 L.Ed.2d 383 (1977)). We have no reason to doubt that NRDC meets the second and third requirements. As to the first, NRDC had to demonstrate that at least one member satisfied the “irreducible constitutional minimum” of standing: injury-in-fact, causation, and redressability. Lujan v. Defenders of Wildlife, 504 U.S. 555, 560, 112 S.Ct. 2130, 119 L.Ed.2d 351 (1992).
NRDC claimed that its members faced increased health risks from EPA’s rule. Although this claim does not fit comfortably within the Supreme Court’s description of what constitutes an “injury in fact” sufficient to confer standing — such injuries must be “actual or imminent, not ‘conjectural’ or ‘hypothetical,’ ” Whitmore v. Arkansas, 495 U.S. 149, 155, 110 S.Ct. 1717, 109 L.Ed.2d 135 (1990) (quoting City of Los Angeles v. Lyons, 461 U.S. 95, 101-02, 103 S.Ct. 1660, 75 L.Ed.2d 675 (1983)) — we have recognized that increases in risk can at times be “injuries in fact” sufficient to confer standing. See Mountain States Legal Found v. Glickman, 92 F.3d 1228, 1234-35 (D.C.Cir.1996). Environmental and health injuries often are purely probabilistic. See NRDC I, 440 F.3d at 483; cf. 520 S. Mich. Ave. Assocs., Ltd. v. Devine, 433 F.3d 961, 962-63 (7th Cir.2006). We have cautioned that this category of injury may be too expansive. “[Wjere all purely speculative ‘increased risks’ deemed injurious, the entire requirement of ‘actual or imminent injury1 would be rendered moot, because all hypothesized, nonimminent ‘injuries’ could be dressed up as ‘increased risk of future injury.’ ” Ctr. for Law & Educ. v. Dep’t of Educ., 396 F.3d 1152, 1161 (D.C.Cir. 2005). We therefore generally require that petitioners demonstrate a “substantial probability” that they will be injured. See Sierru Club, 292 F.3d at 898, 899; Am. Petroleum Inst. v. EPA, 216 F.3d 50, 63-64, 67 (D.C.Cir.2000); La. Envtl. Action Network v. EPA, 172 F.3d 65, 68 (D.C.Cir.1999). Mountain States Legal Foundation v. Glickman, which found that an increased risk of forest fire created by a Forest Service logging rule was enough to support standing, held that the relevant variations in risk must be “nontrivial,” 92 F.3d at 1235, and “sufficient ... to take a suit out of the category of the hypothetical,” id. at 1234-35 (quoting Vill. of Elk Grove Vill. v. Evans, 997 F.2d 328, 329 (7th Cir.1993)).
NRDC’s expert quantified the increased risk posed by EPA’s rule in an affidavit stating that “it is reasonable to expect more than 10 deaths, more than 2,000 nonfatal skin cancer cases, and more than 700 cataract cases to result from the 16.8 million pounds of new production and consumption allowed by the 2005 exemption rule.” Aff. of Dr. Sasha Madronich ¶ 8. Intervenor Methyl Bromide Industry Panel argued that the probability of injury to NRDC’s members is too small. In NRDC I, we found the annualized risk posed to NRDC members to be trivial. 440 F.3d at 481-82 & n. 8, 484. The parties vigorously dispute whether we were correct to hold as a quantitative matter that NRDC’s alleged injury was trivial or whether, in NRDC’s words, any “scientifically demonstrable increase in the threat of death or serious illness,” Pet. for Reh’g or Reh’g En Banc 4, is sufficient for standing. This question has given rise to a conflict among the circuits. Compare Baur v. Veneman, 352 F.3d 625, 634 (2d Cir.2003); Cent. Delta Water Agency v. United States, 306 F.3d 938, 947-48 (9th [229]*229Cir.2002); Friends of the Earth, Inc. v. Gaston Copper Recycling Corp., 204 F.3d 149, 160 (4th Cir.2000) (en banc), with Shain v. Veneman, 376 F.3d 815, 818 (8th Cir.2004); Baur, 352 F.3d at 651 & n. 3 (Pooler, J., dissenting). On reconsideration, we have determined that the question is one we do not have to answer in this case. EPA’s expert, who built the quantitative model on which both sides rely, now informs us that “[ejxpressing the risk in annualized terms is not practical” and “it is more appropriate to express the risk as a population’s cumulative or lifetime risk.”6 Decl. of Reva Rubenstein ¶ 20. The lifetime risk that an individual will develop nonfatal skin cancer as a result of EPA’s rule is about 1 in 200,000 by the intervenor’s lights, see Aff. of Dr. Louis Anthony Cox, Jr. ¶ 13, or 1 in 129,000 by EPA’s, Decl. of Reva Rubenstein ¶¶ 8-9. Even if a quantitative approach is appropriate — an issue on which we express no opinion — this risk is sufficient to support standing. One may infer from the statistical analysis that two to four of NRDC’s nearly half a million members will develop cancer as a result of the rule.
As to causation, NRDC’s asserted injuries are linked to EPA’s action through a fairly straightforward chain: EPA has permitted too much new production and consumption of methyl bromide, which will result in more emissions, which -will increase ozone depletion, which will adversely affect the health of NRDC’s members. This injury can be redressed if EPA does not permit such excessive production and consumption of methyl bromide.
III.
On the merits, NRDC argues that “EPA’s 2005 critical-use rule violates the express terms of the Montreal Protocol Parties’ unanimous Decisions,” Final Opening Br. for Pet’r 20, and therefore is “not in accordance with law.” 42 U.S.C. § 7607(d)(9)(A); see Allied Local & Reg’l Mfrs. Caucus v. EPA, 215 F.3d 61, 68 (D.C.Cir.2000).
Decision Ex.I/3, in which the Parties reached agreement on methyl bromide critical-use exemptions for 2005, stated that the United States had a critical need for 8,942 metric tons of methyl bromide. Id. Annex II.A. To meet this need, the Parties agreed to allow new production and consumption in the amount of 7,659 metric tons, id. Annex II.B, with the remaining critical uses to be met by drawing down existing stocks. Id. ¶ 2. The decision also stated that each Party “which has an agreed critical use should ensure that the criteria in paragraph 1 of decision IX/6 are applied” when implementing the exemption, “and that such procedures take into account available stocks.” Id. ¶ 5 (emphasis added). Paragraph 1 of Decision IX/6 directs the Parties to authorize new production and consumption of methyl bromide only if it “is not available in sufficient quantity and quality from existing stocks,” Decision IX/6 ¶ l(b)(ii), and only after “[a]ll technically and economically feasible steps have been taken to minimize the critical use,” id. ¶ l(b)(i).
NRDC believes EPA’s rule departs from these post-treaty agreements in three respects. First, the rule authorizes 7,659 [230]*230metric tons of new production and consumption — the maximum agreed upon in Decision Ex.I/3 — without offsetting this amount by existing stocks. See Final Rule, 69 Fed.Reg. at 76,989. EPA declined to disclose the size of the total nationwide methyl bromide stockpile, see id. at 76,990 — an action NRDC claims is itself a violation of the Clean Air Act, 42 U.S.C. § 7607(d)(4)(B)(i). Still, the record suggests that the stockpile is at least as large as the United States’ total critical-use allocation for 2005. Second, EPA’s rule allows noncritical users to draw down existing stocks. See Final Rule, 69 Fed.Reg. at 76,987-88. NRDC claims that the “decisions” implicitly reserve the stocks for critical users only. Third, EPA approved 8,942 metric tons of critical uses — again the maximum agreed upon in Decision Ex. 1/3 — without considering anew whether this was the minimum amount feasible. Id. at 76,989. EPA counters that it adhered to the agreed-upon critical-use and new production and consumption levels, and that the remainder of the decisions are “hortatory.” Id. at 76,987.
NRDC fashions the entirety of its argument around the proposition that the “decisions” under the Protocol are “law.” This premise is flawed. The “decisions” of the Parties — post-ratification side agreements reached by consensus among 189 nations — are not “law” within the meaning of the Clean Air Act and are not enforceable in federal court.
The Clean Air Act authorizes EPA to “exempt the production, importation, and consumption of methyl bromide for critical uses” only “[t]o the extent consistent with the Montreal Protocol.” 42 U.S.C. § 7671c(d)(6); see also id. § 7671m(b).7 The Protocol bans the production or consumption of methyl bromide after December 31, 2004, except “to the extent that the Parties decide to permit the level of production or consumption that is necessary to satisfy uses agreed by them to be critical uses.” Montreal Protocol art. 2H(5). NRDC argues that because the Clean Air Act requires EPA to abide by the Protocol, and because the Protocol authorizes future agreements concerning the scope of the critical-use exemption, those future agreements must “define the scope of EPA’s Clean Air Act authority.” Supp. Br. for Pet’r 4.
NRDC’s interpretation raises significant constitutional problems. If the “decisions” are “law” — enforceable in federal court like statutes or legislative rules— then Congress either has delegated lawmaking authority to an international body or authorized amendments to a treaty without presidential signature or Senate ratification, in violation of Article II of the Constitution. The Supreme Court has not determined whether decisions of an international body created by treaty are judicially enforceable. But there is a close analogy in this court. The United States is a party to a treaty establishing the International Court of Justice (ICJ). In Committee of United States Citizens Living in Nicaragua v. Reagan, 859 F.2d 929 (D.C.Cir.1988), we held that rulings of the ICJ do not provide “substantive legal standards for reviewing agency actions,” id. at 942, because the rulings, though authorized by the ratified treaty, were not themselves self-executing treaties. Id. at 937-38; see, e.g., Medellin v. Dretke, 544 U.S. 660, 682-84, 125 S.Ct. 2088, 161 [231]*231L.Ed.2d 982 (2005) (O’Connor, J., dissenting).
Although Committee of United States Citizens is highly suggestive of the outcome in this case, several features of the Montreal Protocol “decisions” may distinguish them from ICJ “adjudications.” For one thing, Congress implemented the Montreal Protocol with a direction to EPA to abide by its terms. See 42 U.S.C. §§ 7671c(d)(6), 7671m(b). For another, Montreal Protocol “decisions” are not adjudications between parties; instead, they purport to set rules for implementing ongoing treaty commitments.
The legal status of “decisions” of this sort appears to be a question of first impression. There is significant debate over the constitutionality of assigning lawmaking functions to international bodies. See, e.g., Julian G. Ku, The Delegation of Federal Power to International Organizations: New Problems with Old Solutions, 85 Minn. L. Rev. 71 (2000); Edward T. Swaine, The Constitutionality of International Delegations, 104 Colum. L. Rev. 1492 (2004). A holding that the Parties’ post-ratification side agreements were “law” would raise serious constitutional questions in light of the nondelegation doctrine, numerous constitutional procedural requirements for making law, and the separation of powers.
We need not confront the “serious likelihood that the statute will be held unconstitutional.” Almendarez-Torres v. United States, 523 U.S. 224, 238, 118 S.Ct. 1219, 140 L.Ed.2d 350 (1998); see also id. at 250, 118 S.Ct. 1219 (Scalia, J., dissenting). It is far more plausible to interpret the Clean Air Act and Montreal Protocol as creating an ongoing international political commitment rather than a delegation of lawmaking authority to annual meetings of the Parties. Cf. Mistretta v. United States, 488 U.S. 361, 373 n. 7, 109 S.Ct. 647, 102 L.Ed.2d 714 (1989).
Nowhere does the Protocol suggest that the Parties’ post-ratification consensus agreements about how to implement the critical-use exemption are binding in domestic courts. The only pertinent language in Article 2H(5) states that the Parties will “decide to permit” production and consumption necessary to satisfy those uses that they “agree[ ]” to be critical uses. The Protocol is silent on any specific conditions accompanying the critical-use exemption. Post-ratification agreements setting these conditions are not the Protocol.
To illustrate, suppose the President signed and the Senate ratified a treaty with Germany and France to conserve fossil fuel. How this is to be accomplished the treaty does not specify. In a later meeting of representatives of the signatory countries at the United Nations, a consensus is reached to lower the speed limits on all major highways of the signatory nations to a maximum of 45 miles per hour. No one would say that United States law has thus been made.
EPA characterizes the decisions as “subsequent consensus agreements of the Parties that address the interpretation and application of the critical use provision .... ” Final Rule, 69 Fed.Reg. at 76,985. This may be so. Like any interpretive tool, however, the “decisions” are useful only to the extent they shed light on ambiguous terms in the Protocol. But the details of the critical-use exemption are not ambiguous. They are nonexistent. The “decisions” do not interpret treaty language. They fill in treaty gaps.
Article 2H(5) thus constitutes an “agreement to agree.” The parties agree in the Protocol to reach an agreement concerning the types of uses for which new production and consumption will be permitted, and the amounts that will be [232]*232permitted. “Agreements to agree” are usually not enforceable in contract. See 1 Richard A. Lord, Williston on Contracts § 3:5, at 223-24 & n.17 (4th ed.1990); cf. El Al Israel Airlines, Ltd. v. Tsui Yuan Tseng, 525 U.S. 155, 167, 119 S.Ct. 662, 142 L.Ed.2d 576 (1999); Zicherman v. Korean Air Lines Co., Ltd., 516 U.S. 217, 226, 116 S.Ct. 629, 133 L.Ed.2d 596 (1996); Foster v. Neilson, 27 U.S. (2 Pet.) 253, 314, 7 L.Ed. 415 (1829) (“A treaty is in its nature a contract between ... nations.”). And the fruits of those agreements are enforceable only to the extent that they themselves are contracts. There is no doubt that the “decisions” are not treaties.
The Parties’ post-ratification actions suggest their common understanding that the decisions are international political commitments rather than judicially enforceable domestic law. See Olympic Airways v. Husain, 540 U.S. 644, 650, 124 S.Ct. 1221, 157 L.Ed.2d 1146 (2004); Tseng, 525 U.S. at 167, 119 S.Ct. 662; Restatement (Third) of Foreign Relations Law of the United States § 325(2) (1987) (“Any subsequent ... practice between the parties in the application of the agreement [is] to be taken into account in its interpretation.”). The Parties met to decide the 2006 critical-use exemptions well after EPA’s rule went into effect. See Second Extraordinary Report, supra note 4. Yet they did not invoke the Protocol’s internal noncompliance procedure against the United States, see Montreal Protocol art. 8, nor did they admonish the United States to change its interpretation of the previous decisions.8 This course of dealing suggests that the Parties intended the side agreements to be enforceable as a political matter at the negotiating table.
Our holding in this case in no way diminishes the power of the Executive to enter into international agreements that constrain its own behavior within the confines of statutory and treaty law. The Executive has the power to implement ongoing collective endeavors with other countries. See Louis Henkin, Foreign Affairs and the United States Constitution 219-20 (2d ed.1996). Without congressional action, however, side agreements reached after a treaty has been ratified are not the law of the land; they are enforceable not through the federal courts, but through international negotiations.
IV.
NRDC claims that EPA violated the Clean Air Act when it failed to disclose the amount of existing domestic stockpiled methyl bromide. See 42 U.S.C. § 7607(d)(4)(B)(i). In doing so, EPA merely followed its own regulation that precluded disclosure of the information pending the resolution of reverse FOIA litigation. See 40 C.F.R. § 2.205(f)(2). NRDC’s own FOIA request for the aggregate stockpile information was denied on this basis. See NRDC v. Leavitt, No. 04-01295, 2006 WL 667327 (D.D.C. Mar.14, 2006). EPA’s actions were in accordance with law and neither arbitrary nor capricious.
* * * * * *
[233]*233Because we now conclude that NRDC has standing to pursue its claim, we grant the petition for rehearing and withdraw our prior opinion. Because the post-ratification agreements of the parties are not “law,” EPA’s rule — even if inconsistent with those agreements — is not in violation of any domestic law within the meaning of the Clean Air Act, 42 U.S.C. § 7607(d)(9)(A), the petition for review is denied.
So ordered.