Opinion for the Court filed by Circuit Judge CLARENCE THOMAS.
CLARENCE THOMAS, Circuit Judge:The United Mine Workers of America challenges a decision of the Assistant Secretary of Labor for Mine Safety and Health granting the petitions of Jim Walter Resources, Inc. to modify a mandatory safety standard. The modification exempts Jim Walter’s Number 3 and Number 4 mines in Jefferson County, Alabama from 30 C.F.R. § 75.1002, which bans the use of high-voltage electrical cables within 150 feet of a mine’s working face. Because the grant of the modification was lawful, we deny the union’s petition for review.
I.
The Federal Mine Safety and Health Act of 1977 sets out interim mandatory health standards, see 30 U.S.C. §§ 841-846, and interim mandatory safety standards, see id. §§ 861-878, for underground coal mines. Section 101(a) of the Act authorizes the Secretary of Labor, through rulemaking, to “develop, promulgate, and revise as may be appropriate, improved mandatory health or safety standards for the protection of life and prevention of injuries in coal or other mines.” Id. § 811(a). Under section 101(c) of the Act, the Secretary may modify the application of any mandatory safety standard to a particular mine if she finds that
an alternative method of achieving the result of such standard exists which will at all times guarantee no less than the same measure of protection afforded the miners of such mine by such standard, or that the application of such standard to such mine will result in a diminution of safety to the miners in such mine.
Id. § 811(c); see also 30 C.F.R. § 44.4(a)(1).1 “The modification, together with any conditions, [has] the same effect as a mandatory safety standard.” Id. § 44.4(c).
II.
Jim Walter Resources, Inc. operates underground coal mines Number 3 and Number 4 in Jefferson County, Alabama. It *272uses the longwall mining system in both mines. A longwall panel is created by digging two parallel, vertical tunnels (the headgate and tailgate entries) and a third horizontal connector (the longwall). See United Mine Workers of Am., Int’l Union v. Dole, 870 F.2d 662, 675 (D.C.Cir.1989). The ceiling of the longwall “exposes the face of rock from which coal will be extracted by a shearer moving back and forth across the face.” Id. Mining begins at the bottom of the parallel entries and progresses back towards ground level. After miners extract all the coal from a longwall panel, the roof caves in.
Jim Walter’s longwall mining equipment runs on electrical power. Electricity enters the mine through a surface substation, which steps down the voltage from 44,000 to 7200 volts. It travels through the mine until it reaches a power center about 150 feet from the longwall face. There, the electricity drops to 995 volts and travels to Jim Walter’s longwall equipment.
Jim Walter wants to operate its longwall equipment with 2300 volts. A mandatory safety standard, however, prohibits Jim Walter from installing the necessary high-voltage cable. Section 75.1002 of title 30 of the Code of Federal Regulations states: “Trolley wires and trolley feeder wires, high-voltage cables and transformers shall not be located inby the last open crosscut and shall be kept at least 150 feet from pillar workings.”2 Regulations of the Mine Safety and Health Administration define anything over 1000 volts as high voltage. See 30 C.F.R. § 75.2(j).
In December 1987, Jim Walter filed with MSHA two petitions to modify the application of 30 C.F.R. § 75.1002 to Mines Number 3 and Number 4. In its petitions, Jim Walter asserted that its proposed high-voltage system would satisfy section 101(c) as “an alternative method” of affording miners “the same measure of protection” that 30 C.F.R. § 75.1002 provides. See 30 U.S.C. § 811(c). The United Mine Workers of America objected to the petitions on the ground that Jim Walter would mine deeper and longer longwall panels with high-voltage power, as well as on the ground that high voltage itself might be unsafe. According to the union, larger longwall panels would increase miners’ exposure to dust and methane, create ventilation problems, and make escape from the mines more difficult.
On May 3, 1988, MSHA issued its proposed decisions and orders granting both petitions, subject to certain conditions. One of the conditions prohibited Jim Walter from mining longwall panels with lengths greater than 900 feet or depths greater than 10,000 feet. The union accepted all of the conditions but sought to add more. It proposed additional stipulations, most of which addressed its dust, methane, ventilation, and escapeway concerns.
An administrative law judge held a hearing then affirmed the proposed decisions and orders, adding only one of the union’s proposed stipulations. First, he explained that the purpose of section 75.1002 is to protect miners “from face and explosive hazards as well as related electrical hazards.” He concluded that the proposed decisions and orders “met if not exceeded” the current standard’s protection against these dangers. Next, the AU rejected the union’s contentions that larger longwalls would increase dust, methane, ventilation, and escapeway hazards. According to the AU, “the Union’s witnesses whol[ly] failed to back their concerns with qualified testimony.”
The Assistant Secretary of Labor for Mine Safety and Health affirmed the AU’s decision. He agreed with the AU that the proposed system might have several electrical safety benefits. He further agreed that the union had failed to prove that the “overall effect” of Jim Walter’s petitions would lessen the protection that section 75.1002 affords miners. Explaining that he was “mindful of the hazards associated with larger longwall panels” and that he had “considered the hazards associated with respirable dust, possible ventilation complications and longer escapeways,” the Assistant Secretary listed three reasons *273why the ALJ had properly rejected the union’s extraelectrical concerns:
First, ... the high-voltage system proposed by Jim Walter is as safe as the medium-voltage system currently in use at the No. 3 and No. 4 mines.
Second, mandatory standards relating to dust, ventilation and escapeways are adequate to control hazards related to larger longwall panels. Those standards will be fully enforced by MSHA at the No. 3 and No. 4 mines____
Third, the record does not contain any credible evidence that Jim Walter will be unable to comply with all applicable dust, ventilation, and escapeway standards in mining longwalls the width and depth permitted in the Proposed Decisions and Orders (900 feet x 10,000 feet)____
In a footnote, he further stated:
In fact, the record establishes the contrary. For example, current regulations for escapeways under 30 C.F.R. 75.1704 do not place distance limitations on designated escape routes. The escape routes available at Jim Walter’s No. 3 and No. 4 Mines are accessible and in good condition. Also, intake air is available a short distance from the longwall face in the tailgate entry, as well as in the designated intake escapeway off the headgate side of the longwall face.
The Assistant Secretary concluded that the union had failed to rebut the “rather considerable evidence” favoring the grant of Jim Walter’s petitions.
III.
In International Union, United Mine Workers of America v. FMSHA, 920 F.2d 960 (D.C.Cir.1990), we explained that the Assistant Secretary reviews “alternative method” petitions in two steps. The first step, “aimed at meeting § 101(c)’s requirement that the alternative “achiev[e] the result’ of the original standard,” involves a determination whether “the modification promote[s] the specific safety goals of the original standard ... with roughly comparable success.” Id. at 963. The second, aimed at meeting section 101(c)’s requirement that the alternative guarantee “the same measure of protection” as the original standard, involves a determination “whether the modification achieves a net gain in mine safety (or at least equivalence), taking all effects into account.” Id. The union contends that the Assistant Secretary’s second-step analysis here was arbitrary and capricious and unsupported by substantial evidence. We disagree.3
Arbitrary and capricious review requires the court to decide whether an “agency [has] examine[d] the relevant data and articulate[d] a satisfactory explanation for its action including a ‘rational connection between the facts found and the choice made.’ ” Motor Vehicle Mfrs. Ass’n v. State Farm Mut. Auto. Ins. Co., 463 U.S. 29, 43, 103 S.Ct. 2856, 2866, 77 L.Ed.2d 443 (1983) (citation omitted). Here we review the Assistant Secretary’s decision that the proposed high-voltage system would ensure net equivalence in overall mine safety.
The union argues that in reaching his decision, the Assistant Secretary did not properly examine evidence of potential safety losses. It points out that although the Assistant Secretary said he was “mindful of” dust, methane, ventilation, and escapeway dangers, he “fail[ed] to articulate exactly what the hazards are and how he considered them in relation to the modification.” But the Assistant Secretary’s lack of precision reflected the union’s failure of proof. The union registered only vague and unsubstantiated assertions on the record, and the Assistant Secretary was not required to look beyond that record. See 30 C.F.R. § 44.35.
The union further argues that even if the Assistant Secretary did consider its safety concerns, he did not adequately explain why those concerns failed to outweigh the evidence of safety benefits. Indeed, parts of the Assistant Secretary’s opinion, read in isolation, might support the union’s contention that his decision was arbitrary. At one point, he justified his rejection of the *274union’s dust, methane, ventilation, and escapeway concerns on the grounds that Jim Walter’s proposed high-voltage system would be “as safe” as its current medium-voltage system and that mandatory standards would “control hazards related to larger longwall panels.” But if Jim Walter’s high-voltage system would only be “as safe” as the medium-voltage system, then any aggravation of dust, methane, ventilation, and escapeway hazards due to larger longwalls would result in a net reduction of mine safety. While mandatory standards might “control hazards,” they would not necessarily prevent an increase in hazards.
Elsewhere in his opinion, however, the Assistant Secretary spoke of “the numerous safety advantages” of Jim Walter’s proposed high-voltage system, and of “the rather considerable evidence in favor of granting the petitions for modification.” He also pointed to the union’s failure to rebut Jim Walter’s prima facie case. The opinion as a whole confirms that the Assistant Secretary balanced the union’s evidence of potential safety losses against Jim Walter’s evidence of potential safety gains. We can easily infer why he found the union’s unsupported concerns less weighty. Though cryptic, his opinion was not arbitrary and capricious. See State Farm, 463 U.S. at 43, 103 S.Ct. at 2866 (“We will ... ‘uphold a decision of less than ideal clarity if the agency’s path may reasonably be discerned.’ ” (citation omitted)).
The Assistant Secretary’s decision also rested on substantial evidence. Before the ALT, Jim Walter presented ample, unrebutted testimony that the proposed high-voltage system would have numerous safety advantages.4 The union then tried, but failed, to show that its dust, methane, ventilation, and escapeway concerns outweighed those advantages. Lacking scientific expertise, the union’s witnesses presented anecdotal evidence and theories grounded in common sense, rather than empirical data or scientific opinions. None of them tried to compare Jim Walter’s safety record at an 850-foot longwall, which it had recently mined, with its record at typical 650-foot longwalls. Nor had any of the union’s witnesses read, much less analyzed, Jim Walter’s most recent ventilation plans. The union failed to present any concrete evidence requiring rebuttal from Jim Walter. Jim Walter’s witnesses nonetheless addressed the union’s various concerns.
The union argued that mining deeper and longer panels would release more methane and dust from the coal beds, increasing the likelihood of ignitions in the mines and lung disease in the miners. Because Jim Walter’s current ventilation and monitoring techniques would not adequately protect against these increased risks, the union further argued, the proposed decisions and orders should contain additional conditions that would.
In rejecting the union’s proposed conditions, the Assistant Secretary adopted an ALJ finding that credited the testimony of John Stevenson, Jim Walter’s General Manager of Ventilation, and MSHA inspectors Tom Meredith and Terry Gaiter. Stevenson testified that most of the dust and methane problems at Jim Walter’s mines are unrelated to the length of a particular longwall. Since dust and methane liberation occurs during the cutting process, and since the shearer cuts coal at the same rate regardless of the longwall’s length, he explained, longer longwalls would not increase the concentration of dust or methane in the mines. Stevenson further testified that Jim Walter planned to use various techniques to control the methane and dust problems at its longwalls. For example, Jim Walter would use a process called horizontal degasification to extract gas from the coal beds at all of its 850-foot long-walls. It also would inject water into the coal to prevent dust from floating off of *275the walls. According to Stevenson, horizontal degasification and pre-wetting had adequately controlled the methane and dust problems at an 850-foot longwall panel in Jim Walter’s Mine Number 7. Both Meredith and Gaiter confirmed significant aspects of Stevenson’s testimony.
The union also argued that larger long-walls would increase escapeway hazards because miners would have a greater distance to travel in order to reach fresh air and to leave the mine. It proposed additional fresh-air intakes and self-contained self-rescuers to improve ventilation in the elongated escapeways.
In rejecting the union’s proposed escape-way stipulations, the Assistant Secretary credited the testimony of Meredith, who explained that the length of the longwalls in Jim Walter’s mines would not limit opportunities for escape. Meredith pointed out that miners on the longwall face could leave the mine through the tailgate area, as well as through the designated headgate entrance. Air is readily available in both passages. In addition, Stevenson pointed out that miners would not have to travel long distances to leave the mines, since none of Jim Walter’s five-year plans showed depths of more than 6000 feet.
The Assistant Secretary weighed the concrete testimony of Jim Walter’s witnesses against the general concerns of the union’s and ruled in favor of Jim Walter. He further explained that even if the union’s concerns were meritorious, regulations other than 30 C.F.R. § 75.1002 would accommodate them. See, e.g., 30 C.F.R. pt. 75 subpt. D (methane and ventilation standards); id. pt. 70 subpt. B (respirable dust standards); id. § 75.1704 to .1704-2, 75.-1707, 75.1714, and 75.1714-3 (escapeway standards). Every six months, Jim Walter must submit for MSHA approval a detailed ventilation system and methane and dust control plan explaining how Jim Walter intends to comply with the dust, methane, and ventilation standards. See id. §§ 75.-316, 75.316-1. An MSHA official testified that the agency would not relax its standards in reviewing those plans, even as longwalls enlarge. The Assistant Secretary’s grant of Jim Walter’s petition thus rested on substantial evidence.
Finally, the union contends that the AU denied it the opportunity to submit relevant evidence at the administrative hearing. We reject this contention as well. Although the AU expressed doubts that he had to consider the union’s non-electrical concerns, he did not exclude evidence on the basis of those doubts. Indeed, the union identifies only two evidentiary rulings made on relevance grounds, neither of which excluded the union’s evidence on dust, methane, ventilation, or escapeway hazards.5 The AU rejected the testimony of other witnesses because they were not competent to testify on the matters that the union wished to prove.6 He acted well within his discretion.
IV.
The petition for review is
Denied.
. The Secretary has delegated her rulemaking and modification powers to the Assistant Secretary for Mine Safety and Health, who heads the Mine Safety and Health Administration. See 29 U.S.C. § 557a.
. The regulation tracks the language in section 310(c) of the Act. See 30 U.S.C. § 870(c).
. Because the Assistant Secretary's second-step analysis survives our review, we do not address MSHA’s assertion that the second step is discretionary under section 101(c).
. Dr. Lloyd Morley, a professor of Mineral Engineering at the University of Alabama, and Ian Davison, the lonjgwall project manager for Jim Walter, testified that the high-voltage system would: (1) make cable overheating and motor failure less likely; (2) afford miners greater protection should a short-circuit occur; (3) require fewer trailing cables; (4) have additional and more sensitive ground-fault protection features; and (5) use cables with higher insulation ratings.
. See J.A. 292-95 (refusing to admit testimony on Jim Walter’s violation of "permissibility” standards for electrical components near mine face); J.A. 318-21 (refusing to admit MSHA citation for failure to guard high-voltage cable properly).
. See, e.g., J.A. 282-84 (forbidding witness from testifying about theoretical matters because union had failed to lay foundation as to his scientific expertise); J.A. 301, 308-09 (forbidding witness from testifying about optimal placement of methane monitors and overall effect of Jim Walter’s application because he lacked requisite expertise).