Appellant officials of the State of South Dakota and Charles Mix County filed petitions for rehearing and rehearing en banc of the court’s August 25, 2009 decision in this matter. The Yankton Sioux Tribe and the United States filed their individual responses to the petitions on January 25, 2010, supporting the court’s decision and judgment. Now before the court are the petitions for panel rehearing.
In the meantime we have permitted amici to file six briefs in support of the petitions 1 and granted a motion by the state *987appellants to file a supplement to their petition. Still pending are motions by the Rosebud Sioux Tribe to file an amicus brief opposing the petitions and by the county appellants to file a supplemental petition for rehearing and rehearing en banc. The United States and the Yankton Sioux Tribe have filed oppositions to the county appellants’ motion, which was filed the same day as the responses to the original petitions. The Tribe has also argued that the new factual materials submitted by the state appellants in their petition and the supplement thereto should be stricken.
Recently petitioners filed a joint motion on April 6, 2010 seeking leave to amend their petitions for rehearing to include new arguments based on City of Sherrill v. Oneida Indian Nation, 544 U.S. 197, 217-21, 125 S.Ct. 1478, 161 L.Ed.2d 386 (2005), and also proposing that the court “remand this case to the district court to allow the district court an opportunity to consider {City of Sherrill ], or in the alternative, determine the case in [their] favor ... or, in the further alternative, allow the parties to fully brief the issues for the panel and the Court.” Motion to Support Proposed Amendment to State and County Petitions for Rehearing and Rehearing en Banc at 1. The Tribe and the United States filed responses in opposition to this belated motion on April 16, 2010.
Petitioners based their original requests for rehearing on two primary grounds. They object to some language in our 2009 opinion touching on former allotments within the original boundaries of the Yank-ton Sioux Reservation which were patented in fee after 1948. Petitioners also renew their earlier unsuccessful arguments that the Yankton Sioux Reservation has been disestablished, continuing to disagree with the decision to the contrary reached more than ten years ago after extensive litigation in Yankton Sioux Tribe v. Gaffey (Gaffey II), 188 F.3d 1010 (8th Cir.1999), reh’g and reh’g en banc denied, cert. denied, 530 U.S. 1261, 120 S.Ct. 2717, 147 L.Ed.2d 982 (2000).
What petitioners have generally not done in their petitions for rehearing is to attack the judgment actually rendered by the court on August 25, 2009. Instead, they raise a virtual smokescreen by focusing on dicta in a single footnote of our 37 page decision.2 The second and third sentences of that footnote are the basis from which petitioners mount their attack, but these sentences did not speak to any matter actually litigated or decided in this case. Nor was such language ever incorporated into our judgment which only determined the status of trust lands within the former boundaries of the Yankton Sioux Reservation, our judgment in Gaffey II having determined that the reservation had never been disestablished.
That petitioners are well aware of the limited scope of our judgment is evidenced by the county’s letter proposing that the language which they attack be added to the court’s judgment. Letter from Tom D. Tobin to Michael E. Gans, Clerk of Court (Nov. 5, 2009) (noting that the proposition that “allotments patented in fee since 1948 and now held by non-Indians continue to be Indian country under the terms of 18 U.S.C. § 1151(a) ... does not appear to be included or set forth in the paragraph at the conclusion of the opinion” and requesting that the clerk bring that *988“possible oversight” to the attention of the court). In drafting the judgment in Part V of the August 2009 opinion the court acted intentionally in stating all matters it actually decided in this case.
In sum, petitioners raise objections to issues which the court did not decide and which are beyond the scope of this litigation. They raise concerns about the possible consequences of a decision which the court has not reached. Since the language on which petitioners have focused is extraneous to what was actually decided by the court, we will grant the petitions for rehearing for the limited purpose of withdrawing the opinion filed on August 25, 2009 and replacing it with a revised opinion. The revised opinion contains the identical judgment but eliminates footnote 10 and several textual asides touching on matters not litigated or decided, but which have possibly been misunderstood.
I.
The long history of this litigation which began in 1994 is set out in detail in our decision. Yankton Sioux Tribe v. Podhradsky (Podhradsky II), 577 F.3d 951, 959-60 (8th Cir.2009). The latest chapter of the case was initiated by our 1999 remand to the district court in Gajfey II, a decision on which the Supreme Court denied certiorari. Gajfey II held that the Yankton Sioux Reservation was never disestablished and that some original agency lands identified by the Supreme Court in South Dakota v. Yankton Sioux Tribe, 522 U.S. 329, 350, 118 S.Ct. 789, 139 L.Ed.2d 773 (1998), remained part of a continuing reservation. See Gaffey II, 188 F.3d at 1030. We observed that the record before the court was inadequate to “define the precise limits” of the remaining reservation, particularly with respect to lands within the original boundaries of the reservation which were held in trust. Id. We therefore remanded for the district court to develop a record concerning such trust lands. Id. at 1030-31.
After our remand the district court held a trial3 and then determined that three categories of trust lands remain part of the Yankton Sioux Reservation under 18 U.S.C. § 1151(a): (1) land which was reserved to the federal government in the 1894 Act and then subsequently returned to the Tribe; (2) land which had been allotted to individual Indians and was still held in trust; and (3) land which was taken into trust under the Indian Reorganization Act of 1934. Yankton Sioux Tribe v. Podhradsky (Podhradsky I), 529 F.Supp.2d 1040, 1058 (D.S.D.2007). These conclusions fit squarely within the scope of our remand order. The district court went beyond the specific directions of our mandate in one respect, however, in that it also addressed land continuously owned in fee by individual Indians. The district court concluded that such land remained part of the reservation and denied all other claims for relief. Id. Both sides appealed.
Our subsequent opinion affirmed the judgment of the district court in respect to each category of trust land and affirmed its alternative holding that miscellaneous trust lands were a dependent Indian community under § 1151(b). Podhradsky II, 577 F.3d at 974. We vacated one portion of the district court’s judgment, however. That portion which held that fee lands continuously owned by Indians were part of the diminished reservation was vacated *989because the record remained inadequate to determine the status of such lands. Id. at 972, 974. Finally, we affirmed the denial of all other claims. Id. at 974.
Our mandate to the district court in Gaffey II, the district court’s judgment on remand in Podhradsky I, and our judgment on this appeal (Podhradsky II) concerned specific, discrete issues — namely, the status of some 37,000 acres of trust land within the original boundaries of the Yankton Sioux Reservation. The only other category of land ruled on by the district court was fee land continuously owned by Indians, and we vacated that part of the district court’s judgment. Our own August 2009 judgment in Podhradsky II was explicitly limited to trust lands.
II.
Rather than focusing on the actual judgment, petitioners focus on the undeveloped suggestion in footnote 10 of our opinion that 18 U.S.C. § 1151(a) might be applied to former allotments patented in fee after the statute’s enactment in 1948. By claiming that the presence of this hypothesis unrelated to our holdings and never incorporated into our conclusions or judgment “abruptly transformed the status of at least 7,250 acres of land,” petitioners have raised a straw man to attack. State Appellants’ Petition for Rehearing and Petition for Rehearing En Banc at 1. They have then spun out some possible consequences if the court had decided what they protest, raising fears about land owned by local government entities such as the Wagner Community School District and the Wagner Fire Protection District. See Charles Mix County’s Petition for Rehearing and Petition for Rehearing En Banc at 8. Their amici go further in claiming “devastating effects” if the Yankton Sioux Tribe were able to impose taxes and various regulations on non Indian landowners. Brief of Leonard Kreeger et al. as Amicus Curiae in Support of State and County Petitions at 4-5.
In their responses neither the Tribe nor the United States focus on footnote 10, but they assert that petitioners’ fears are overblown. The Tribe argues that speculation about any potential future impact is not a sufficient basis for rehearing. The United States points out that “[djespite a decade of experience with a post-Gajfey checkerboard Reservation, this area of South Dakota has not experienced any of the problems described by the State, County or amici.” United States’ Response to the Petitions for Panel Rehearing Filed by the State of South Dakota and Charles Mix County at 4 n. 2.
We need not address each individual point petitioners raise because they are well aware that the wording to which they object is not part of the judgment in this case, as evidenced by the county’s suggestion for its incorporation. The status of fee lands not owned by Indians was not considered or decided by the district court, nor was the issue litigated on appeal. The record remains inadequate to decide the status of such lands, just as it was inadequate to decide the status of Indian owned fee lands. See Podhradsky II, 577 F.3d at 971-72. The final two sentences in footnote 10 and other extraneous language were in the nature of a hypothetical reflection stimulated by study of shifting federal Indian policy over the years. Because these dicta were not incorporated into the judgment, they are not binding upon the parties and do not provide a reason to revisit the substance of our decision. See Coen v. American Sur. Co. of New York, 120 F.2d 393, 400 (8th Cir.1941); In re Bridgestone/Firestone, Inc. Tires Prods. Liab. Litig., 333 F.3d 763, 766 (7th Cir.2003); cf. ACLU of N.J. v. Schundler, 168 F.3d 92, 98 n. 6 (3d Cir.1999) (standards for rehearing en banc “look to the panel’s
*990decision, not to the panel’s dicta”) (emphasis in original). They should therefore be eliminated from the decision.
III.
The second ground upon which petitioners seek rehearing is their continuing effort to disestablish the Yankton Sioux Reservation. In South Dakota v. Yankton Sioux Tribe, the Supreme Court declined to adopt their proposition that the reservation was disestablished by the 1894 congressional ratification of an agreement with the Tribe that ceded certain reservation lands to the United States. 522 U.S. at 357-58, 118 S.Ct. 354. The Court also declined to answer the question of whether the Yankton Sioux Reservation had been diminished beyond the loss of those unallotted lands specifically severed in the agreement. Id. Instead, the Court recognized arguments on both sides of the issues and remanded the question for determination by the lower courts. Since the Supreme Court’s decision, petitioners have unsuccessfully pressed their disestablishment argument twice before the district court, see Yankton Sioux Tribe v. Gaffey (Gaffey I), 14 F.Supp.2d 1135, 1137 (D.S.D.1998); Podhradsky I, 529 F.Supp.2d at 1043-44, and twice before this court, see Gaffey II, 188 F.3d at 1015; Podhradsky II, 577 F.3d at 961.
At each level their disestablishment arguments have been squarely rejected after thorough study of the record and exhaustive consideration of the precedents. Gajfey II’s 1999 holding that the Yankton Sioux Reservation was never legally disestablished is the law of the case. See Podhradsky II, 577 F.3d at 962-63. We also note that the Supreme Court chose not to grant certiorari on the issue in 2000. Petitioners have again failed to show that the court’s decision was incorrect. Moreover, they have pointed to no facts or legal authority previously overlooked by the court which would support reconsideration of that determination. “The purpose of a petition for rehearing ... is to direct the Court’s attention to some material matter of law or fact which it has overlooked in deciding a case, and which, had it been given consideration, would probably have brought about a different result.” NLRB v. Brown & Root, Inc., 206 F.2d 73, 74 (8th Cir.1953); see also Fed. R.App. P. 40(a)(2); 16A Charles Alan Wright, Arthur R, Miller, & Edward H. Cooper, Federal Practice & Procedure § 3986.1 (4th ed. 2008) (“It should go without saying that a petition for rehearing should not be filed simply to reargue matters already argued unsuccessfully in the original appeal proceedings.”).
Petitioners do seek support for their disestablishment argument in a recent Tenth Circuit decision, Osage Nation v. Irby, 597 F.3d 1117 (10th Cir.2010). In Osage Nation, the Nation sought a declaration that its members residing and employed in Osage County, Oklahoma were exempt from paying state income tax because the county was still Indian country. See id. at 1120. The court concluded, however, that the Osage Nation’s former reservation had been disestablished by a 1906 Act of Congress. Id. That 1906 statute has no equivalent in the history of the Yankton Sioux, and the respondents argue that Osage Nation is not in any way inconsistent with our decision in this case. We agree.
Osage Nation addressed a unique surplus land act and a reservation with a historical context unlike that of the Yank-ton Sioux Reservation. Applying familiar legal principles, the Tenth Circuit discerned from the circumstances surrounding the passage of the Osage Allotment Act that there was “clear congressional intent and Osage understanding that the reservation would be disestablished.” Id. at *9911124. In contrast, the 1894 Act which ceded surplus land from the Yankton Sioux Reservation reflected the parties’ intent to “preserv[e] the support of the federal government and its superintendence over [the allotted] lands.” Podhradsky II, 577 F.3d at 966 (citing Report of the Yankton Indian Commission (Mar. 31, 1893), reprinted in S. Exec. Doc. No. 27, 53d Cong., 2d Sess., 7, 17 (1894)).
Neither the language of the 1894 Act dealing with the land of the Yankton Sioux Reservation nor the circumstances surrounding its passage evinced a clear congressional intent to disestablish the reservation. Absent such clear intent, the reservation remains for “[o]nce a block of land is set aside for an Indian Reservation ... [it] retains its reservation status until Congress explicitly indicates otherwise.” Solem v. Bartlett, 465 U.S. 463, 470, 104 S.Ct. 1161, 79 L.Ed.2d 443 (1984) (emphasis added). Osage Nation in fact supports our decision in Podhradsky II, for it recognized that “Congress’s intent to terminate [a reservation] must be clearly-expressed, and there is a presumption in favor of the continued existence of a reservation.” Osage Nation, 597 F.3d at 1122 (citing Yankton Sioux Tribe, 522 U.S. at 343, 118 S.Ct. 789 and Solem, 465 U.S. at 472, 104 S.Ct. 1161).
IV.
The state appellants also seek rehearing on the ground that the court wrongly determined that lands within the former boundaries of the Yankton Sioux Reservation which were taken into trust under the Indian Reorganization Act are part of the reservation under § 1151(a). They argue that under 25 U.S.C. § 467, such reacquired lands cannot become part of a reservation unless the Secretary of the Interi- or has made a formal proclamation to that effect. Petitioners also claim that our decision conflicts with United States v. Stands, 105 F.3d 1565 (8th Cir.1997). As the United States points out, however, these contentions essentially recapitulate arguments already raised and correctly addressed on appeal. See Podhradsky II, 577 F.3d at 968-69.
As we have explained, 25 U.S.C. § 467 does not require a proclamation from the Secretary when that official “decides to add land to a preexisting reservation such as that of the Yankton Sioux.” Id. at 969. Rather, the statute authorizes the Secretary both “to proclaim new Indian reservations ... or to add such lands to existing reservations.” Id. at 968-69. (quoting 25 U.S.C. § 467) (emphasis in original). Congress thus explicitly provided for land to be added to existing reservations without a proclamation. Because the IRA trust lands in this case were simply returned to an existing reservation, no proclamation was necessary to restore their reservation status.
Petitioners rely on Stands for the proposition that “tribal trust land beyond the boundaries of a reservation is ordinarily not Indian country.” Stands, 105 F.3d at 1572. This argument was directly addressed in our decision. See Podhradsky II, 577 F.3d at 968 n. 13. The language in Stands on which petitioners rely is classic dicta. The question on which the case turned was not whether any trust lands were part of a reservation, but simply whether a particular plot of land was “an Indian allotment, the Indian title to which has not been extinguished.” Stands, 105 F.3d at 1571. The Stands court neither considered nor decided matters bearing directly on the status of the IRA trust lands in this case.
The petitions for rehearing merely reiterate arguments related to the IRA trust lands which were already soundly rejected on appeal, and they consequently fail to satisfy the standards for panel rehearing.
*992V.
We turn finally to the pending motions. Despite over fifteen years of litigation and the voluminous record in this case, petitioners now seek to add more factual information in support of their petitions. To that end, the state appellants filed with their petition for rehearing six maps intended to illustrate the jurisdictional changes wrought at various stages of this litigation. Only two of these maps were previously in the record (maps D and E). The county appellants also filed copies of each of these maps with their petition, along with an affidavit of Jo Ann Mazourek, the Director of Equalization for Charles Mix County, summarizing her examination of records relating to former allotments patented in fee after 1948.
On January 13, 2010 we granted the state appellants’ motion to file a supplement to their petition containing a revised affidavit by Ms. Mazourek stating that 8,939.47 acres of land left allotted status and were patented in fee after the 1948 enactment of 18 U.S.C. § 1151, and Map G, which shows the locations of those fee parcels. Her affidavit also suggests that, based upon her assessment of whether the titleholder has an Indian name or not, over 90 percent of that fee land is not owned by Indians today.
The county appellants also moved on January 25, 2010 to file a supplemental petition for rehearing and for rehearing en banc. That supplemental petition included additional argument attacking the court’s decision, copies of the revised Mazourek affidavit and Map G, 22 pages of quoted excerpts from various treatises and judicial opinions, and an excerpt from the transcript of the 1998 oral argument before the Supreme Court in South Dakota v. Yankton Sioux Tribe.
The Tribe argues that the maps and affidavits not in the record when the court reached its decision must be stricken. We agree. New factual material may be considered on a petition for rehearing only in the rarest circumstances. See Smith v. Armontrout, 865 F.2d 1502, 1505 n. 5 (8th Cir.1988). This case falls within the rule, not the exception, particularly because the proposed new information concerns matters not decided by the court or necessary to its decision. Accordingly, maps A, B, C, F, and G, and the Mazourek affidavits should be stricken from the record.
The Tribe and the United States also argue that the county appellants’ motion to file a supplemental petition for rehearing should be denied. The factual exhibits included with the county’s supplemental petition were already filed by the state appellants with their supplement. Aside from those duplicative materials, the supplemental petition largely restates earlier arguments and seeks to buttress them with extensive unanalyzed quotations from legal texts. To the limited extent the supplemental petition offers new arguments, there is no apparent reason they could not have been included in the original petition. We see no reason to permit the filing of what amounts to an overlength petition more than two months after the already extended filing deadline. To do so would unnecessarily prolong this already extended process. The county appellants’ motion should therefore be denied.
The Rosebud Sioux Tribe’s motion for leave to file an amicus brief should be granted, just as were the motions of the amici supporting petitioners.
Finally, petitioners’ April 2010 motion to enlarge their petitions must be denied. In that motion, petitioners argue that City of Sherrill supports both their disestablishment claim and their claim that former allotments patented in fee after 1948 are not part of the reservation. As to the first issue, the Tribe points out that the lands at *993issue in City of Sherrill were located in an area with less than one percent Indian population and out of Indian hands for some 200 years. City of Sherrill, 544 U.S. at 211, 216, 125 S.Ct. 1478.
We need not examine the significant differences between City of Sherrill and the present case in any detail because it is far too late for petitioners to present an entirely new theory in support of disestablishment. Petitioners have not previously relied upon that 2005 case, nor did they raise the equitable doctrines on which it relies in the district court, on appeal, or even in their petitions for rehearing. “Panel rehearing is not a vehicle for presenting new arguments,” Easley v. Reuss, 532 F.3d 592, 593-94 (7th Cir.2008) (per curiam), and we do not ordinarily consider arguments raised for the first time in a petition for rehearing, see In re Hen House Interstate, Inc., 177 F.3d 719, 724-25 (8th Cir.1999) (en banc). Petitioners have had years to develop their litigation strategy, and City of Sherrill was decided more than two years before the parties briefed the merits of the current dispute in the district court. Petitioners “can not now, after failing to prevail on [their] original theories, invoke an entirely new theory in support of’ their position. United States v. Klotz, 503 F.2d 1056, 1056 (8th Cir.1974) (per curiam). As for the post 1948 fee lands, their status was not part of our 1999 remand to the district court (or its decision) and was not determined in our 2009 decision and judgment. Petitioners’ recent motion for a renewed remand to the district court thus seeks not only to raise a new argument, but entirely new claims related to a category of lands not at issue below or on appeal. It of course remains open to the parties to file new actions in the district court if they choose. A remand to the district court of issues beyond the scope of this lengthy litigation would be wholly inappropriate.
VI.
This order as well as the amended opinion will moot some issues in the current petitions for rehearing and rehearing en banc. All of the parties should therefore have the opportunity to file any new petitions within 45 days from the entry of this order and of the amended opinion.
VI.
For the foregoing reasons it is hereby ordered that:
(1) The petitions for panel rehearing are granted to the extent that the dicta discussed herein shall be stricken from the court’s opinion filed in this case on August 25, 2009;
(2) The opinion filed in this matter on August 25, 2009 and reported at 577 F.3d 951 is withdrawn and our amended opinion shall be substituted and filed concurrently with this order;
(3) The Rosebud Sioux Tribe’s motion for leave to file an amicus brief is granted;
(4) The motion of Charles Mix County for leave to file a supplemental petition for rehearing is denied;
(5) Maps A, B, C, F, and G, and the affidavits of Jo Ann Mazourek filed with the petitions for rehearing and the state appellants’ supplement are stricken from the record; and
(6) Petitioners’ Motion For Leave To Amend The Petitions For Rehearing Is Denied. The Requests In The Motion For Decision In Petitioners’ Favor, Remand, Or Further Briefing Are Also Denied.
(7) Any new petitions for rehearing and rehearing en banc shall be filed with*994in 45 days of the entry of this order and of the amended opinion.
. The amici supporting the petitions are the Charles Mix Electric Association, several South Dakota counties which include former Indian allotments, the Wagner Community School District, the Southern Missouri Waste Management District, several cities within the original boundaries of the Yankton Sioux Reservation, and a number of individuals who own land within the original boundaries of the reservation.
. Footnote 10 in the opinion read as follows: It is unclear from the record whether any allotments have been patented in fee since 1948 and subsequently sold to white owners. If such lands exist, however, they would continue to be Indian country under the clear terms of § 1151(a). The holding in Gaffey II that lands which passed into white ownership lost reservation status thus only applies to pre 1948 conveyances.
. During a two day trial the district court took testimony and admitted numerous documents. The record includes thousands of pages relating to more than 150 tracts of land, including deeds, title reports, and correspondence concerning BIA management of the trust lands. It also includes numerous maps as well as legislative and administrative materials related to the reservation and its status to relevant federal authorities.