
606 F.3d 676 (2010)
WORLD WIDE RUSH, LLC, a Pennsylvania limited liability company; Insite Outdoor Works LA, LLC, a Delaware limited liability company, Plaintiffs-Appellees,
v.
CITY OF LOS ANGELES, a California municipal corporation, Defendant-Appellant.
Sky Tag, Inc., a California corporation; Sky Tag West, Inc., a California corporation; Sunset & Vine, Inc., a California corporation; West Hollywood Inc., a California corporation; Sky Creative Services, Inc., a California corporation; Sky Posters Inc., a California corporation, Plaintiffs-Appellees,
v.
City of Los Angeles, a California Charter city, Defendant-Appellant.
Wilshire Center, LLC, a Delaware limited liability company; Jamison 1055 Wilshire, LLC, a California limited liability company; Wilmont, LLC, a Delaware limited liability company; Equitable Plaza, LLC, a California limited liability company; 3545 Wilshire, LLC, a California limited liability company; Metroplex, LLC, a California limited liability company; 3600 Wilshire, LLC, a California limited liability company; 3699 Wilshire, LLC, a California limited liability company; 4041 Wilshire, LLC, a California limited liability company; 4055 Wilshire, LLC, a California limited liability company; 4201 Wilshire, LLC, a California limited liability *677 company; Jamison 5455 Wilshire, LLC, a California limited liability company; West Wilshire Medical Center, LLC, a California limited liability company; 9800 La Cienega, LLC, a California limited liability company; Fairfax Business Center, LLC, a California limited liability company; 7080 Hollywood, LLC, a Delaware limited liability company; 700 Flower Plaza, LLC, a California limited liability company company; 4929 Wilshire, LP, a Delaware limited partnership; 3575 Cahuenga, LLC, a California limited liability company; 1900 Westwood, LLC, a California limited liability; 933 N. La Brea, LLC, a Delaware limited liability company; Royal Beverly Glen Plaza, LLC, a California limited liability company; 1055 Seventh, LLC, a California limited liability company; 6380 Wilshire, LLC, a California limited liability company; 11620 Wilshire, LLC, a California limited liability company; 3875 Wilshire, LLC, a California limited liability company; 16501 Ventura, LLC, a California limited liability company; 17000 Ventura, LLC, a California limited liability company; 22801 Ventura, LLC, a California limited liability company, Plaintiffs-Appellees,
v.
City of Los Angeles, a California Charter city, Defendant-Appellant.
Nos. 08-56454, 08-56523, 09-55494, 09-55792, 09-55791.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted December 10, 2009.
Filed May 26, 2010.
*679 Carmen A. Trutanich, Rockard J. Delgadillo, Jeri L. Burge, Kenneth T. Fong, Tayo A. Popoola, and Michael J. Bostrom of the Office of the City Attorney, Los Angeles, CA, for defendant-appellant City of Los Angeles.
Rex S. Heinke, Michael C. Small, L. Rachel Helyar, Maria Ellinikos, and Christopher Blanchard of Akin, Gump, Strauss, Hauer & Feld, LLP, Los Angeles, CA, and Paul E. Fisher of the Law Offices of Paul E. Fisher, Newport Beach, CA, for plaintiffs-appellees World Wide Rush, LLC, et al.
Gary S. Mobley of Case, Knowlson & Jordan, LLP, Newport Beach, CA, for plaintiffs-appellees Sky Tag, Inc., et al.
Philip R. Recht and Andrew T. Kugler of Mayer Brown, LLP, Los Angeles, CA, for amicus curiae Community Redevelopment Association, LLC.
Michael Jenkins and Gregg Kovacevich of Jenkins & Hogin, LLP, Manhattan Beach, CA, for amicus curiae League of California Cities.
Luis Li, Allison B. Stein, and Jenny M. Jiang of Munger, Tolles & Olson, LLP, Los Angeles, CA, for amicus curiae Van Wagner Communications.
Before: STEPHEN REINHARDT, STEPHEN S. TROTT and KIM McLANE WARDLAW, Circuit Judges.
WARDLAW, Circuit Judge:
The City of Los Angeles ("City") appeals the grant of summary judgment in favor of World Wide Rush and Insite Outdoor *680 Works LA (collectively "WWR") and the entry of injunctions in favor of WWR and Wilshire Center, Jamison, and Sky Tag (collectively "Sky Tag") enjoining enforcement of certain billboard regulations. We must decide whether the district court erred in concluding that (1) the City's Freeway Facing Sign Ban is an unconstitutionally underinclusive restriction on commercial speech and (2) the City's Supergraphic and Off-Site Sign Bans are unconstitutional prior restraints on speech. Because the City's exceptions to the Freeway Facing Sign Ban do not undermine the City's asserted interests in enacting the Ban, and because the City Council's authority to create exceptions to the Supergraphic and Off-Site Sign Bans is a permissible aspect of its inherent legislative discretion, we reverse.
The City also appeals the district court's order finding it in civil contempt of the injunction against enforcement of the Freeway Facing Sign Ban and the Supergraphic and Off-Site Sign Bans as to WWR's billboards. Because we vacate the injunction, we also reverse the contempt order.
Finally, we affirm the district court's decision to allow just one round of amendments to the pleadings as a proper exercise of its discretion.

BACKGROUND
"The story of billboards in America is... characterized by an ongoing struggle between an expanding industry and a resistant public." David Burnett, Note, Judging the Aesthetics of Billboards, 23 J.L. & Pol. 171, 174 (2007). One of the first chapters in this story played out in Saint Louis in 1911, when the Missouri Supreme Court was called upon to decide whether cities had the power to regulate billboards at all. See St. Louis Gunning Adver. Co. v. City of St. Louis, 235 Mo. 99, 137 S.W. 929, 941 (1911). At that time, billboards were "temporary affairs" constructed from "upright timbers, or posts set in the ground" and "braced from the rear, with stringers running from one to the other." Id. at 941-42. They were described as "inartistic" and "unsightly" monstrosities that were "liable to be blown down and to fall upon and injure those who may happen to be in their vicinity." Id. It was even said that they were "hiding places and retreats for criminals and all classes of miscreants." Id. The Missouri Supreme Court had little trouble concluding that "this class of advertising as now conducted" was "subject to control and regulation by the police power of the state." Id. at 942.
Of course, not everyone shared this view. One author described billboards of that era as "thing[s] of beauty" that bore "work of artistic and pleasing character, framed in a structure of tasteful design." Frank Presbrey, The History and Development of Advertising 503-04 (1929). Decades later, in an essay detailing the history of outdoor advertising, the President of the Outdoor Advertising Association of America described billboards as "an important business tool" and emphasized that their "influence reaches the people in every city and town without getting in their way." Phillip Tocker, Standardized Outdoor Advertising: A History, Economics and Self-Regulation, in Outdoor Advertising: History and Regulation 56 (1969). He even argued that billboards "assisted communities ... in beautifying areas." Id. at 53. "All that [the billboard industry] asks in return," he pleaded, "is to continue to do business where others do business, under the same freedoms and limitations." Id. at 56.
These appeals present the latest chapter in "the story of billboards." No longer tied to wooden posts protruding from holes *681 in the ground, in modern-day cities such as Los Angeles, today's billboards may be projected onto or hung from the sides of skyscrapers or strategically located near main traffic arteries so that they are visible from great distances by masses of would-be consumers. Their labels alone (e.g., "supergraphic signs") conjure up a setting far removed from Saint Louis in the early 1900s. As the nature of billboards has changed, so too has the nature of the legal problems they present. The question of the day is no longer whether cities may regulate billboards at all, but is instead the extent to which they may do so consistent with the First Amendment guarantee of freedom of expression.

I. The City's Sign Regulations
The City regulates signs, including billboards, through Chapter I, Article 4.4 of the Los Angeles Municipal Code ("LAMC"). Article 4.4's stated purpose is to "promote public safety and welfare" by "provid[ing] reasonable protection to the visual environment" and by ensuring that billboards do not "interfere with traffic safety or otherwise endanger public safety." LAMC § 14.4.1. Article 4.4 prohibits some types of billboards and restricts the size, placement, and illumination of others. These appeals arise from First Amendment challenges to certain content-neutral provisions of Article 4.4: the "Freeway Facing Sign Ban" and the "Supergraphic and OffSite Sign Bans."

A. Freeway Facing Sign Ban
Article 4.4's Freeway Facing Sign Ban prohibits billboards located within 2,000 feet of and "viewed primarily from" a freeway or an on-ramp/off-ramp. LAMC § 14.4.6(A). Notwithstanding the Freeway Facing Sign Ban, the City has permitted freeway-facing billboards in some circumstances, two of which are applicable here.[1] First, in 1999, the City adopted an ordinance authorizing billboards near the Staples Center, a state-of-the-art sports and entertainment complex that was developed to eliminate blight and dangerous conditions in downtown Los Angeles. See Los Angeles, Cal., Ordinance No. 172465 (1999). The City asserted that the nature of the Staples Center's use, coupled with its location in the center of a highly urbanized area, required billboards that could effectively communicate event-related information. Id. Today, there are several freeway facing billboards near the Staples Center, including some that use flashing displays and frequently changing digital content.
The City made another exception to the Freeway Facing Sign Ban in 2008, when it undertook plans to renovate Santa Monica Boulevard with the aim of improving the flow of traffic between the 405 Freeway and the Beverly Hills border. See Los Angeles, Cal., Ordinance No. 179827 (2008). However, the targeted traffic corridor *682 was home to sixteen billboards, the outright elimination of which might have triggered the City's obligation to compensate the billboards' owners under California's eminent domain law. See Cal. Bus. & Prof.Code § 5412. To avoid the requirements of takings law, including the obligation of just compensation, the City agreed with the billboard owners that four sign faces could be relocated to a newly created special use district ("SUD") near Fifteenth Street. While the relocated billboards would face a freeway, the Fifteenth Street SUD resulted in a net reduction of billboards in the City.

B. Supergraphic and Off-Site Sign Bans
Supergraphic billboards are large-format signs projected onto or hung from building walls. See LAMC § 14.4.2. They are often made of large vinyl or mesh canvasses, which are hung with cables from the sides of buildings. Id. Off-site billboards display messages directing attention to a business or product not located on the same premises as the sign itself. Id. For example, a billboard promoting the latest blockbuster movie, but attached to a furniture store, is an off-site sign. The same billboard, when attached to a theater playing the movie, is an on-site sign. Article 4.4 contains the Supergraphic and Off-Site Sign Bans, which prohibit these types of billboards. Id. §§ 14.4.4(B)(9), (11).
However, the Supergraphic and Off-Site Sign Bans exempt "signs that are specifically permitted pursuant to a legally adopted specific plan, supplemental use district or an approved development agreement." Id. A "specific plan" is a land use plan that provides details for the implementation of the City's general land use plan. See id. § 11.5.7(A) ("A specific plan shall provide by ordinance regulatory controls or incentives for the systematic execution of the General Plan."); see also Cal. Gov't Code § 65450. A SUD is a land use planning device employed to "regulate and restrict the location of certain types of uses whose requirements are difficult to anticipate and cannot adequately be provided for in the" City's general zoning plan. LAMC § 12.32(S)(1)(a). "Sign districts," like the Fifteenth Street SUD discussed above, are among the recognized types of SUDs. Id. § 13.11. Finally, a "development agreement" is a mechanism by which the City may provide a developer with certainty that existing rules, policies, and regulations will continue to govern his project once it has been approved. See Cal. Gov't Code § 65864.
The Supergraphic and Off-Site Sign Bans do not specify the circumstances under which any of these exceptions may be invoked, but other laws provide that SUDs and development agreements must not conflict with specific plans, which, in turn, must not conflict with the City's general plan. See Cal. Gov't Code § 65454 (specific plans); id. § 65867.5(b) (development agreements); LAMC § 13.11(C) (SUDs). The authority to employ each exception to the Supergraphic and Off-Site Sign Bans derives, not from Article 4.4, but from the City's legislative power to control local land use. See Cal. Gov't Code § 65867.5(a) (development agreements); LAMC § 11.5.7(A) (specific plans); id. § 12.32 (land use legislative actions); id. § 13.11(B) (SUDs); Los Angeles, Cal., City Charter § 558 (procedures for adoption of land use ordinance).

II. Procedural History
WWR sued to enjoin enforcement of the Freeway Facing Sign Ban and the Supergraphic and Off-Site Sign Bans. First, relying on Central Hudson Gas & Electric Corp. v. Public Service Commission of New York, 447 U.S. 557, 100 S.Ct. 2343, 65 *683 L.Ed.2d 341 (1980), WWR argued that the Freeway Facing Sign Ban is an unconstitutionally underinclusive restriction on commercial speech because the City had, in fact, permitted some freeway facing billboards despite the Ban. Second, WWR challenged the Supergraphic and Off-Site Sign Bans as facially unconstitutional prior restraints on speech. It argued that the exceptions to the Bans vest the City Council with unbridled discretion to select among preferred speakers because those exceptions lack objective criteria for their application.
WWR did not assert a Central Hudson challenge to the Supergraphic and Off-Site Sign Bans even though the district court granted leave to amend the complaint more than one year into the litigation and several months after the scheduling order's deadline. In granting leave at that late juncture, the district court warned that it would not entertain any further amendments to the pleadings, which "should have been settled long ago." After that, WWR did not seek leave to raise new legal theories.
The district court granted WWR summary judgment on its First Amendment claims. See World Wide Rush, LLC v. City of Los Angeles, 579 F.Supp.2d 1311 (C.D.Cal.2008) ("World Wide Rush I"). It concluded that the Freeway Facing Sign Ban violates the First Amendment because the City's decisions to allow freeway facing billboards at the Staples Center and in the 15th Street SUD undermine its stated interests in safety and aesthetics. Id. at 1328. It ruled that "preserving even one freeway-facing sign" was fatal to the Freeway Facing Sign Ban. Id. The district court also concluded that the Supergraphic and Off-Site Sign Bans violate the First Amendment because "the City can avoid the blanket ban on off-site and supergraphic signs simply by enacting a specific plan in a certain area, but there are no standards that would prevent the City from enacting a specific plan because it wishes to approve particular speech or a particular speaker." Id. at 1319. Further, it found that the requirement that SUDs and development agreements conform to specific plans is "a loophole that eviscerates the standards" governing SUDs and development agreements. Id. at 1321. The district court concluded, "The City has set up a system that allows it to eliminate speech based on content." Id. Accordingly, the district court entered an order enjoining the City from enforcing the Freeway Facing Sign Ban and the Supergraphic and Off-Site Sign Bans as to WWR's billboards.
The City thereafter decided that several of WWR's supergraphic billboards violated other Article 4.4 provisions not covered by the district court's injunction. For instance, the City cited WWR for violations of Article 4.4's regulations restricting the size of "wall signs" and for failing to obtain proper permits for several billboards. Faced with the new citations, WWR returned to the district court, arguing that the City was using other provisions of Article 4.4 to circumvent the district court's order and that it could not obtain the necessary permits because the City continued to enforce the invalidated provisions. The district court concluded that the City improperly had denied WWR permits and issued WWR citations under the guise of other Article 4.4 provisions, when, in fact, the City was continuing to enforce the Supergraphic and Off-Site Sign Bans in contravention of the injunction. World Wide Rush, LLC v. City of Los Angeles, 605 F.Supp.2d 1088, 1105-11 (C.D.Cal. 2009) ("World Wide Rush II"). The district court found the City in civil contempt and required it to discharge certain citations. Id. at 1111-12.
*684 Meanwhile, other billboard companies got in on the action. As the district court explained, "Not long [after issuance of the World Wide Rush I injunction], numerous billboard companies began putting Supergraphic Signs up all over Los Angeles.... As a result, well-traveled thoroughfares that contained any sort of sizable building were soon pockmarked with Supergraphic Signs." Id. at 1092. The City responded in kind by adopting a complete moratorium on new supergraphic and off-site signs. See Los Angeles, Cal., Ordinance No. 180445 (2008). Some billboard companies, including Sky Tag, filed copycat lawsuits, in which they sought injunctions to protect their own billboards from City enforcement efforts. For the reasons announced in the World Wide Rush I opinion, the district court enjoined the City from enforcing the Supergraphic and Off-Site Sign Bans as to certain of Sky Tag's billboards. See World Wide Rush II at 1112-14.
The City appeals the district court's grant of summary judgment and an injunction in favor of WWR in World Wide Rush I. It also appeals the civil contempt judgment and injunction in favor of Sky Tag in World Wide Rush II. WWR appeals the district court's refusal to entertain any further amendments, supplements, or changes to its complaint after granting leave to file its amended and supplemental complaint.
The district court exercised jurisdiction under 28 U.S.C. § 1331. We have jurisdiction under 28 U.S.C. § 1291. "We review de novo the constitutionality of a local ordinance." G.K. Ltd. Travel v. City of Lake Oswego, 436 F.3d 1064, 1070 (9th Cir.2006). "We review for abuse of discretion the district court's civil contempt order." Hook v. Ariz. Dep't of Corrs., 107 F.3d 1397, 1403 (9th Cir.1997). We review for abuse of discretion the district court's decisions as to amendments to the complaint. See Gardner v. Martino, 563 F.3d 981, 990 (9th Cir.2009).

DISCUSSION

I. Constitutionality of the Sign Regulations
Courts have "often faced the problem of applying the broad principles of the First Amendment to unique forms of expression.... Each method of communicating ideas is a law unto itself and that law must reflect the differing natures, values, abuses and dangers of each method. We deal here with the law of billboards." Metromedia, Inc. v. City of San Diego, 453 U.S. 490, 500-01, 101 S.Ct. 2882, 69 L.Ed.2d 800 (1981) (citations, footnote, and internal quotation marks omitted).

A. Freeway Facing Sign Ban
"In Central Hudson, the Supreme Court announced a four-part test for assessing the constitutionality of a restriction on commercial speech: (1) if `the communication is neither misleading nor related to unlawful activity,' then it merits First Amendment scrutiny as a threshold matter; in order for the restriction to withstand such scrutiny, (2)'[t]he State must assert a substantial interest to be achieved by restrictions on commercial speech;' (3) `the restriction must directly advance the state interest involved;' and (4) it must not be `more extensive than is necessary to serve that interest.'" Metro Lights, L.L.C. v. City of Los Angeles, 551 F.3d 898, 903 (9th Cir.2009) (quoting Cent. Hudson, 447 U.S. at 564-66, 100 S.Ct. 2343), cert. denied ___ U.S. ___, 130 S.Ct. 1014, ___ L.Ed.2d ___ (2009). "[T]he last two steps of the Central Hudson analysis basically involve a consideration of the `fit' between the legislature's ends and the means chosen to accomplish those ends." *685 Rubin v. Coors Brewing Co., 514 U.S. 476, 486, 115 S.Ct. 1585, 131 L.Ed.2d 532 (1995) (internal quotation marks omitted).
As a general matter, there is no question that restrictions on billboards advance cities' substantial interests in aesthetics and safety. Metromedia, 453 U.S. at 508-10, 101 S.Ct. 2882; Metro Lights, 551 F.3d at 904. However, a city "may diminish the credibility of [its] rationale for restricting speech in the first place" where it exempts some speech from the general restriction. Metro Lights, 551 F.3d at 905 (internal quotation marks omitted). The critical question is whether the City "denigrates its interest in ... safety and beauty and defeats its own case by permitting" freeway facing billboards at the Staples Center and in the Fifteenth Street SUD while forbidding other freeway facing billboards. Metromedia, 453 U.S. at 510-11, 101 S.Ct. 2882. "To put it in the context of the Central Hudson test, a regulation may have exceptions that undermine and counteract the interest the government claims it adopted the law to further; such a regulation cannot directly and materially advance its aim," and is, therefore, unconstitutionally underinclusive. Metro Lights, 551 F.3d at 905 (quoting Rubin, 514 U.S. at 489, 115 S.Ct. 1585); see also Greater New Orleans Broad. Ass'n, Inc. v. United States, 527 U.S. 173, 190-93, 119 S.Ct. 1923, 144 L.Ed.2d 161 (1999) (a regulation may be unconstitutionally underinclusive if it "is so pierced by exceptions and inconsistencies" that it cannot advance the government's interest in the regulation).
Here, the City's exceptions to the Freeway Facing Sign Ban do not undermine the City's interests in aesthetics and safety. Indeed, the exceptions were made for the express purpose of advancing those very interests. Allowing billboards at the Staples Center was an important element of a project to remove blight and dangerous conditions from downtown Los Angeles. Similarly, the Fifteenth Street SUD was an outgrowth of the City's efforts to improve traffic flow, and thereby safety, on Santa Monica Boulevard. Not only did the agreement to allow signs in the Fifteenth Street SUD advance that project, it also resulted in a net reduction of billboards in the City. Ironically, the most significant denigration to the City's interests in traffic safety and aesthetics might result, not from allowing the freeway facing billboards at the Staples Center and in the Fifteenth Street SUD, but instead from strict adherence to the Freeway Facing Sign Ban, which might have severely hampered, if not completely defeated, both projects.
The district court took an all-or-nothing approach to its constitutional analysis of the Freeway Facing Sign Ban, stating that to "preserv[e] even one freeway-facing sign ... undermines the City's stated interests in traffic safety and aesthetics." World Wide Rush I, 579 F.Supp.2d at 1328. Our First Amendment jurisprudence, however, contemplates some judicial "deference for a municipality's reasonably graduated response to different aspects of a problem." Metro Lights, 551 F.3d at 910. As the Supreme Court has explained, "It does not follow from the fact that the city has concluded that some commercial interests outweigh its municipal interests in this context that it must give similar weight to all other commercial advertising." Metromedia, 453 U.S. at 512, 101 S.Ct. 2882. Moreover, exceptions to the Freeway Facing Sign Ban must be considered holistically, not in isolation. Again, the Supreme Court has explained, "[T]he effect of the challenged restriction on commercial speech ha[s] to be evaluated in the context of the entire regulatory scheme, rather than in isolation." Greater New Orleans, *686 527 U.S. at 192, 119 S.Ct. 1923; see also Metro Lights, L.L.C., 551 F.3d at 904 ("[W]e must look at whether the City's ban advances its interest in its general application, not specifically with respect to Metro Lights.").
"[E]valuated in the context of the entire regulatory scheme," the challenged exceptions to the Freeway Facing Sign Ban do not render the Ban "so pierced by exceptions and inconsistencies" as to be unconstitutionally underinclusive. Greater New Orleans, 527 U.S. at 190-92, 119 S.Ct. 1923. The City reasonably may have concluded that, on balance, safer and more attractive thoroughfares would result from renovations to Santa Monica Boulevard and a reduction in the City's total number of billboards, even if this required installation of some freeway facing billboards along Fifteenth Street. The City also reasonably may have concluded that the benefits of redeveloping and attracting people to an otherwise dangerous and blighted downtown area outweighed the harm of additional freeway facing billboards restricted to that area. See, e.g., Metro Lights, 551 F.3d at 911 (even with some exceptions, sign ban "went a long way toward cleaning up the clutter, which the City believed to be a worthy legislative goal").
In concluding otherwise, the district court relied on the Supreme Court's decision in Greater New Orleans. There, the Court concluded that a federal regulation prohibiting advertisements for gambling in private casinos but allowing advertisements for gambling on reservations violated the First Amendment. Greater New Orleans, 527 U.S. at 177-79, 119 S.Ct. 1923. Greater New Orleans is inapposite, however, because the regulatory distinction between the two types of casinos counteracted the government's purported interest in minimizing gambling. As the Greater New Orleans Court explained, allowing one type of advertising while prohibiting the other would merely channel gamblers to the reservations, thus rendering the regulation "squarely at odds with the governmental interests asserted in this case." Id. The Freeway Facing Sign Ban is not a means by which the evil sought to be prohibited is simply channeled elsewhere, at odds with the asserted governmental interests. Rather, the City submitted a convincing rationalewhich is entirely consistent with its asserted governmental interestfor exempting some freeway facing signs from its Ban.
The other cases upon which WWR relies are similarly inapposite. In each of those cases, the government created a distinction between permissible and prohibited forms of commercial speech, and, in each case, the distinction undermined the government's asserted interests in the regulation as a whole. See Rubin, 514 U.S. at 489, 115 S.Ct. 1585 ("There is little chance that § 205(e)(2) can directly and materially advance its aim, while other provisions of the same Act directly undermine and counteract its effects."); City of Cincinnati v. Discovery Network, Inc., 507 U.S. 410, 417-18, 113 S.Ct. 1505, 123 L.Ed.2d 99 (1993) (no "reasonable fit" between government interests and regulation which required removal of 62 newsracks but allowed 1,500 to 2,000 to remain); Ballen v. City of Redmond, 466 F.3d 736, 743 (9th Cir.2006) (exceptions to sign ban "compromise the City's interests" in traffic safety and aesthetics). Here, by contrast, the City permitted billboards at the Staples Center and in the Fifteenth Street SUD precisely because of its interests in safety and aesthetics. In addition, the exceptions to the Freeway Facing Sign Ban are content-neutral, whereas the distinctions employed in Greater New Orleans (private casinos versus reservation casinos), Rubin (beer labels versus wine labels), Discovery *687 Network (commercial newsracks versus non-commercial newsracks), and Ballen (content-based exceptions to ban) implicated the messages communicated by the signs at issue. See Metro Lights, 551 F.3d at 904-05 ("[A] regulation can be unconstitutional if it in effect restricts too little speech because its exemptions discriminate on the basis of the signs' messages.") (internal quotation marks omitted); Ballen, 466 F.3d at 743 ("[T]he City's use of a content-based ban rather than a valid time, place, or manner restriction indicates that the City has not carefully calculated the costs and benefits associated with the burden on speech imposed by its discriminatory, content-based prohibition.").
Our recent decision in Metro Lights, in which we rejected a Central Hudson challenge to an LAMC provision banning off-site signs generally, but permitting them on bus shelters, is more analogous.[2]Metro Lights, 551 F.3d at 900-01. Relying on Metromedia, we approved the City's justification for the bus shelter advertisement exception that "proliferation of offsite advertising by numerous and disparate private parties creates more distracting ugliness than a single, controlled series of advertisements on city property over which the City wields contractual supervision." Id. at 910. We concluded that "the specific exception in question here does not weaken the direct link between the City's objectives and its general prohibition of offsite advertising." Id.; see also Outdoor Sys., Inc. v. City of Mesa, 997 F.2d 604, 611 (9th Cir.1993) ("[T]here is a reasonable fit between the sign codes and the interests they seek to achieve."); Clear Channel Outdoor, Inc. v. City of New York, 594 F.3d 94, 110 (2d Cir.2010) ("The City may legitimately allow limited and controlled advertising on street furniture, while also reducing clutter on City sidewalks. Allowing some signs does not constitutionally require a city to allow all similar signs."). Here, as in Metro Lights, the City's decision to permit some freeway facing billboards at the Staples Center and in the Fifteenth Street SUD does not break the link between the Freeway Facing Sign Ban and the City's objectives in traffic safety and aesthetics.

B. Supergraphic and Off-Site Sign Bans
Under the prior restraint doctrine, "a law cannot condition the free exercise of First Amendment rights on the unbridled discretion of government officials." Desert Outdoor Adver. v. City of Moreno Valley, 103 F.3d 814, 818 (9th Cir.1996) (internal quotation marks omitted). "Regulations must contain narrow, objective, and definite standards to guide the licensing authority and must require the official to provide an explanation for his decision." Long Beach Area Peace Network v. City of Long Beach, 574 F.3d 1011, 1025 (9th Cir.2009) (internal quotation marks, citations, and alterations omitted); see also Seattle Affiliate of the Oct. 22nd Coal. to Stop Police Brutality v. City of Seattle, 550 F.3d 788, 798 (9th Cir.2008) (ordinance must have "narrowly drawn, reasonable and definite standards that guide the hand of the administrator"). The district court concluded that the Supergraphic and Off-Site Sign Bans were unconstitutional prior restraints on speech because their exceptions impermissibly vest the City Council with unbridled discretion to select among speakers on the basis of content. This legal conclusion was *688 erroneous, however, because the prior restraint doctrine does not apply to the legislative function at issue here. The exceptions to the Supergraphic and Off-Site Sign Bans are rooted in the City Council's legislative discretion, not its discretion to make executive decisions as part of the LAMC's regulatory scheme. This distinction makes all the difference.
"Unbridled discretion challenges typically arise when discretion is delegated to an administrator, police officer, or other executive official," as opposed to a legislative body. Long Beach Area Peace Network, 574 F.3d at 1042; see, e.g., Thomas v. Chi. Park Dist., 534 U.S. 316, 319-20, 122 S.Ct. 775, 151 L.Ed.2d 783 (2002) (superintendent of park district); City of Lakewood v. Plain Dealer Publ'g Co., 486 U.S. 750, 753, 108 S.Ct. 2138, 100 L.Ed.2d 771 (1988) (mayor); Outdoor Media Group, Inc. v. City of Beaumont, 506 F.3d 896, 904 (9th Cir.2007) (planning director); G.K. Ltd. Travel, 436 F.3d at 1082 (permitting official); Desert Outdoor Adver., 103 F.3d at 818-19 (city official). In rare circumstances, however, a legislative body's reservation of authority could constitute an unconstitutional prior restraint on speech. As we recently explained:
[W]here a legislative body has enacted a permitting scheme for expressive conduct but has reserved some decisionmaking authority for itself under that scheme, that reserved authority is vulnerable to challenge on grounds of unbridled discretion.
Long Beach Area Peace Network, 574 F.3d at 1042. The First Amendment requires standards to cabin the legislative body's authority to execute aspects of the regulatory scheme in such circumstances because that authority "is distinct from the general discretion a legislative body has to enact (or not enact) laws." Id.
This is not that rare circumstance in which the legislative body created a licensing power and reserved it for itself. The City Council's authority to enact special plans, create SUDS, or enter into development agreements derives from its regular and well-recognized legislative power to regulate land use. It does not depend upon or derive from the Supergraphic and Off-Site Sign Bans. The City Council would have the power to employ any of those land use tools even if none was ever mentioned in the Bans; the Bans do no more than affirm the existence of these legislative powers. The First Amendment is not implicated by the City Council's exercise of legislative judgment in these circumstances.
Our recent decision in Long Beach Area Peace Network is illustrative. There, the city enacted a regulatory scheme by which permits would be issued for certain gatherings in public places. See Long Beach Area Peace Network, 574 F.3d at 1025-26. The city council retained the ability to waive permit fees, but the ordinance did not provide standards to cabin the council's exercise of that authority. Id. at 1041. The ordinance was subject to attack under the prior restraint doctrine because the city council's authority was "unlike its usual legislative authority." Id. at 1042. Instead, that authority derived exclusively from the permitting scheme:
Absent a preexisting permitting scheme, a city council could not in advance impose service charges or other fees on a group seeking to hold a demonstration in a public forum.
Id. Here, by contrast, the City Council does have the authority to employ specific plans, SUDs, and development agreements absent the Supergraphic and Off-Site Sign Bans. Because the prior restraint doctrine does not require the City to restrict "the general discretion a legislative body has to *689 enact (or not enact) laws," the district court erred in concluding that the Supergraphic and Off-Site Sign Bans are unconstitutional prior restraints on speech. Id.

II. Injunction and Contempt
"[A] person subject to an injunction must ordinarily obey it." Irwin v. Mascott, 370 F.3d 924, 931 (9th Cir.2004) (discussing Walker v. City of Birmingham, 388 U.S. 307, 87 S.Ct. 1824, 18 L.Ed.2d 1210 (1967)). However, one may challenge an injunction with which one disagrees "through the usual processes of law, such as an appeal." Id. The City appropriately took that approach here, appealing the underlying injunction as well as the order finding it in contempt. Vacatur of the injunction entered in World Wide Rush I voids the civil contempt order entered in World Wide Rush II. See United States v. United Mine Workers of Am., 330 U.S. 258, 295, 67 S.Ct. 677, 91 L.Ed. 884 (1947) ("The right to remedial relief falls with an injunction which events prove was erroneously issued."); Kirkland v. Legion Ins. Co., 343 F.3d 1135, 1142-43 (9th Cir.2003) ("Because entering the order to pay was an abuse of discretion, the corresponding contempt order cannot stand."); Davies v. Grossmont Union High Sch. Dist., 930 F.2d 1390, 1394 (9th Cir.1991) ("[T]he legitimacy of the contempt adjudication is based on the validity of the underlying order.").

III. Amendments to the Pleadings
WWR could have, but failed to, assert a Central Hudson challenge to the Supergraphic and Off-Site Sign Bans. WWR argues that this is so because the district court abused its discretion in curtailing amendments to the pleadings. We disagree.
On January 7, 2007, WWR filed its initial complaint, which the district court would later describe as, "to put it mildly, disorganized." Following a motion to dismiss, the district court concluded that WWR could proceed on allegations that the LAMC impermissibly vested unbridled discretion in a Cultural Affairs Committee and a Community Redevelopment Agency and on a facial challenge to the LAMC's "Hazard to Traffic" provision, which is distinct from the Freeway Facing Sign Ban. See LAMC § 14.4.5. The initial complaint did not contain a Central Hudson challenge to the Freeway Facing Sign Ban or a prior restraint challenge to the Supergraphic and Off-Site Sign Bans. The scheduling order's September 24, 2007, deadline for amending the pleadings came and went without activity. As the district court stated, "This should have settled the pleadings." It did not.
On January 14, 2008, WWR moved for a preliminary injunction, raising for the first time its Central Hudson challenge to the Freeway Facing Sign Ban and its unconstitutional prior restraint challenge to the Supergraphic and Off-Site Sign Bans. On April 3, 2008, instead of denying WWR's preliminary injunction motion for raising claims beyond the scope of the complaint, the district court extended the deadline for amendments to the pleadings to May 5, 2008, and accepted WWR's amended complaint, which incorporated its new First Amendment claims. At that time, the district court admonished the parties that it would not entertain any further amendments to the pleadings after May 5, noting that "the pleadings should have been settled long ago." The new May 5, 2008, deadline for amending the pleadings came and went without further activity; WWR never sought leave for further amendments.
Specifically, WWR never moved for leave to add to its complaint a Central Hudson challenge to the Supergraphic *690 and Off-Site Sign Bans. The district court could not rule on a motion that WWR never made, and we reject WWR's attempt to appeal a nonexistent denial of a nonexistent motion. Given the absence of an adverse ruling from which it may appeal, WWR argues that it would have been futile to seek leave to amend the complaint in light of the district court's statement that such requests would not be entertained. We do not share WWR's view that the district court's admonition was an excuse for WWR's failure to at least proffer a proposed amendment to the pleadings. Assuming, however, that the panel may consider the language of the district court's April 3 order as a de facto prospective denial of motions to amend the pleadings, WWR's argument still fails. The district court's discretion to deny leave to amend is particularly broad where a plaintiff previously has amended the complaint. See Zucco Partners, LLC v. Digimarc Corp., 552 F.3d 981, 1007 (9th Cir.2009). Here, WWR already had been given leave to amend the complaint more than a year into the litigation and several months after passage of the scheduling order's deadline. The district court understandably was wary of further delays. WWR advances no reasonmuch less a good reasonfor its failure to amend its complaint to include a Central Hudson challenge to the Supergraphic and Off-Site Sign Bans. This oversight is particularly inexcusable given that WWR was aware of the possibility of a Central Hudson claim (as evident from its challenge to the Freeway Facing Sign Ban) and was aware of the Supergraphic and Off-Site Sign Bans (as evident from its unbridled discretion challenge to those Bans).

CONCLUSION
The district court erred in holding that the billboards at the Staples Center and in the Fifteenth Street SUD render the Freeway Facing Sign Ban an unconstitutionally underinclusive restriction on commercial speech under Central Hudson. The district court also erred in concluding that the Supergraphic and Off-Site Sign Bans are unconstitutional prior restraints on speech. We therefore REVERSE the grant of summary judgment in favor of WWR and VACATE the injunctions in favor of WWR and Sky Tag. We also REVERSE the district court's order finding the City in civil contempt of the injunction as to WWR's billboards. We AFFIRM the district court's order amending the scheduling order and admonishing the parties that future amendments would not be entertained.
AFFIRMED in part; REVERSED and VACATED in part.
NOTES
[1]  In proceedings before the district court, WWR identified three other freeway-facing billboards to support its challenge to the Freeway Facing Sign Ban. On appeal, however, WWR fails to discuss two of those billboards and thus waives its argument that they undermine the Freeway Facing Sign Ban. See James River Ins. Co. v. Hebert Schenk, P.C., 523 F.3d 915, 920 n. 1 (9th Cir.2008) (waiver of arguments not adequately presented in briefs). A third freeway-facing set of signs depicts members of the Los Angeles Chamber Orchestra. WWR concedes that consideration of these signs is unnecessary to resolution of its constitutional claim and explains that the parties' real quarrel over these signs is whether they are subject to the LAMC at all. The district court did not resolve this issue, and it is not properly presented to us in these appeals. Therefore, our analysis is limited to the two billboard locations on which WWR rests its First Amendment challenge to the Freeway Facing Sign Ban.
[2]  The district court did not have the benefit of our decision in Metro Lights when it decided World Wide Rush I. In World Wide Rush II, the district court rejected the City's argument that Metro Lights abrogated the district court's decision in World Wide Rush I. See World Wide Rush II, 605 F.Supp.2d at 1016.
