OPINION OF THE COURT
NYGAARD, Circuit Judge.Appellant, John W. Dreher, was convicted in the New Jersey state courts of murdering his wife. He is currently serving a sentence of life imprisonment with a minimum term of thirty years before eligibility for parole. He sought a writ of habeas corpus in the U.S. District Court for the District of New Jersey alleging violations of his rights under the Fifth, Sixth and Fourteenth Amendments to the U.S. Constitution, which was denied. Dreher v. Pinchak, No. 98-4816 (D.N.J. filed July 17, 2001). The District Court granted Dreher a certificate of appealability. We conclude that there are unexhausted issues and will remand the matter to the District Court for it to vacate its order and dismiss the petition without prejudice.
I. Factual and Procedural Background
The facts and procedure of this case are detailed at great length in two opinions of the Appellate Division of the New Jersey Superior Court, and in the District Court’s opinion. See State v. Dreher, 302 N.J.Super. 408, 695 A.2d 672 (1997) (Dreher II), cert. denied, sub nom Dreher v. New Jersey, 524 U.S. 943, 118 S.Ct. 2353, 141 L.Ed.2d 723 (1998); State v. Dreher, 251 N.J.Super. 300, 598 A.2d 216 (1991) (Dreher I); Dreher v. Pinchak, No. 98-4816 *802(D.N.J. filed July 17, 2001). Therefore, we need only summarize the factual background relevant to our discussion.
Petitioner’s wife, Gail Dreher, was found dead in the basement of the couple’s home on January 2, 1986. That afternoon, John Dreher reported the crime to the Chatham Township Police Department as a burglary and murder. The autopsy revealed that the cause of death was ligature strangulation, and that Gail Dreher also sustained several head wounds and stab wounds to the back and neck. The autopsy also revealed a single sperm cell in the victim’s nose. The time of the victim’s death was disputed at trial, with the state medical examiner estimating that the victim died between 7:00 and 8:00 a.m., and petitioner contending that death occurred closer to 11:00 a.m.
As the investigation into Gail Dreher’s murder progressed, Petitioner and his mistress, Nance Seifrit, became the primary suspects. Seifrit was arrested in August of 1986, received a grant of immunity, and became the key witness in the prosecution’s case against Petitioner. At trial, Seifrit testified that she and the Petitioner had agreed to confront the victim with the news of their affair on the morning of the murder. Seifrit testified that this confrontation did not go well; that the Petitioner attacked and killed his wife; and that she and the Petitioner removed items from the house to make the crime appear as a burglary. Petitioner’s theory of the case is that Nance Seifrit and a male accomplice, possibly her brother Nathan Seifrit, murdered the victim so that Seifrit could then marry the Petitioner.
Petitioner was convicted in his first trial. The conviction, however, was reversed on appeal and remanded for a new trial because the trial court erred by admitting hearsay statements and allowing improper references to hearsay to be made during the prosecutor’s closing argument. Dreher I, 598 A.2d at 216. Petitioner was indicted a second time and again convicted. This second conviction was confirmed on appeal. Dreher II, 695 A.2d at 672.
II. Exhaustion
Before addressing the merits of a petition for writ of habeas corpus, we have an obligation to determine whether we have appropriate jurisdiction and whether the claims set forth in the petition have been properly exhausted. Federal courts have jurisdiction to review petitions for habeas corpus filed by persons in state custody claiming that they “[are] in custody in violation of the Constitution or laws or treaties of the United States.” 28 U.S.C. § 2254(a). We exercise this jurisdiction only where it “appears that the applicant has exhausted the remedies available in the courts of the State.” McCandless v. Vaughn, 172 F.3d 255, 260 (3d Cir.1999) (citing Walker v. Vaughn, 53 F.3d 609, 614 (3d Cir.1995)).
Although exhaustion can be waived, a State “shall not be deemed to have waived the exhaustion requirement or be estopped from reliance upon the requirements unless the State, through counsel, expressly waives the requirement.” 28 U.S.C. § 2254(b)(3). The requirement that the State “expressly waive” exhaustion is a new one. See Carpenter v. Vaughn, 296 F.3d 138, 146 (3d Cir.2002). Indeed, 28 U.S.C. § 2254(b)(3) specifically mentions exhaustion as the only defense the State must expressly waive. See also Lurie v. Wittner, 228 F.3d 113, 123 (2d Cir.2000). After oral argument, we ordered additional briefing on the question of whether the State had expressly waived the exhaustion requirement in this case. Although the State admitted that it conceded exhaustion in its answer to the petition for writ of habeas corpus, on appeal *803the State argued that it has not expressly waived exhaustion within the meaning of 28 U.S.C. § 2254(b)(3). The Petitioner maintains all his claims have been properly exhausted. We are therefore faced with the initial question of whether the State’s actions can be considered an express waiver.
We have previously noted that “under AEDPA, a District Court may no longer infer that a state has waived the nonexhaustion defense from its failure to invoke the defense expressly.” Lambert v. Blackwell, 134 F.3d 506, 514 (3d Cir.1997). In George v. Sively, a case involving the appeal of a defendant’s conviction under Virgin Islands territorial law, we stated in a footnote that “the United States Attorney has argued that we should hear this appeal and should not require George to exhaust his territorial remedies, but because counsel has not in so many words waived exhaustion, we cannot deem the requirement waived.” 254 F.3d 438, 441 n. 4 (3d Cir. 2001). This language would indicate that, for waiver to be effective, something more than a concession in an answer is required. While we have yet to encounter a situation such as this one (where exhaustion was conceded before the District Court but contested on appeal), our precedent suggests that the standard for proving an express waiver is fairly stringent.
A stringent standard for proving waiver of exhaustion is squarely in line with the underlying purposes of the exhaustion requirement. We recently reviewed these policy justifications in Lambert, where we noted that the Supreme Court has endorsed “rigorous enforcement” of the total exhaustion rule because of “the preference among federal jurists to allow state courts the initial opportunity to review and correct alleged violations of federal constitutional rights.” 134 F.3d at 513. This preference is rooted in principles of comity and judicial efficiency. As we have said, “the doctrine of comity ‘teaches that one court should defer action on causes within its jurisdiction until the courts of another sovereignty with concurrent powers, and already cognizant of the litigation, have had an opportunity to pass upon the matter.’ ” Id. at 513 n. 18 (quoting Rose v. Lundy, 455 U.S. 509, 519, 102 S.Ct. 1198, 71 L.Ed.2d 379 (1982)). As for judicial efficiency, “adoption of a total exhaustion rule causes a reduction in piecemeal litigation, thereby increasing the likelihood that all claims will be reviewed in single proceeding.” Id. at 513.1 These policy justifications counsel against holding that the State of New Jersey expressly waived the defense of nonexhaustion.
Moreover, the exhaustion doctrine also requires that habeas petitioners “fairly present” federal claims to state courts before bringing them into federal court. See Duncan v. Henry, 513 U.S. 364, 366, 115 S.Ct. 887, 130 L.Ed.2d 865 (1995); Picard v. Connor, 404 U.S. 270, 275, 92 S.Ct. 509, 30 L.Ed.2d 438 (1971); Keller v. Larkins, 251 F.3d 408, 413 (3d Cir.2000); Lambert v. Blackwell, 134 F.3d 506, 513 (3d Cir.1997). To “fairly present” a federal claim to a state court, a petition must have presented the claim’s factual and legal substance to the state courts in a manner that puts them on notice that a federal claim is being asserted. McCandless, 172 F.3d at 261. The Supreme Court has instructed that “it is not sufficient that all the facts necessary to support the federal claim *804were before the state courts.” Anderson v. Harless, 459 U.S. 4, 6, 103 S.Ct. 276, 74 L.Ed.2d 3, (1982). Likewise, a “mere similarity” of claims is not sufficient to satisfy exhaustion. See Duncan, 513 U.S. at 366. As the Court explained:
Exhaustion of state remedies required that petitioners “fairly present” federal claims to the state courts in order to give the State the opportunity to pass upon and correct alleged violations of its prisoners’ federal rights. If state courts are to be given the opportunity to correct alleged violations of prisoners’ federal rights, they must surely be alerted to the fact that the prisoners are asserting claims under the United States Constitution. If a habeas petitioner wishes to claim that an evidentiary ruling at a state court denied him the due process of law guaranteed by the Fourteenth Amendment, he must say so, not only in federal court, but in state court.
Id. at 365-66 (citations and quotations omitted).
The District Court found all of the claims raised by the Petitioner to have been fairly presented: “Petitioner has properly exhausted his state remedies. All of the grounds asserted by petitioner in support of his application for habeas corpus were previously presented in his appeal to the New Jersey state courts, triggering the standard of review provided by 28 U.S.C. § 2254(d).” This determination is subject to plenary review. See Whitney v. Horn, 280 F.3d 240, 249 (3d Cir.2002) (citing Schandelmeier v. Cunningham, 819 F.2d 52 (3d Cir.1986)). After a detailed review of the state court record in this case and of the additional submissions we requested of the parties, we find one claim raised in Dreher’s petition which has not been fairly presented to the state courts. Therefore, this claim is not exhausted.
III. The Unexhausted Claim: admission of Dr. Tucker’s testimony on time of death.
Scientific research has demonstrated that after death has occurred, the cells in the retina and tissue surrounding the eye begin to break down. This cellular degradation releases potassium in the vitreous humor. Dr. John I. Coe developed a test and devised a graph using this process, which has since become widely accepted and distributed to all medical examiners in the United States. See Dreher II, 659 A.2d at 462. It is possible to estimate the time of death by comparing the amount of vitreous potassium found in the eye to Dr. Coe’s graph.
Petitioner argues that the trial court erred in allowing the Morris County Medical examiner, Dr. Ernest Tucker, to testify concerning the time of Gail Dreher’s death because Tucker used a methodology for which there was no scientific basis. Coe’s graph assumed a linear degradation whereas Dr. Tucker maintains that the coordinates resulting from the research do not form a straight line, but instead form a curve which suggests a larger range of possible times of death. Using his own methodology, Dr. Tucker insisted that Gail Dreher died at approximately 7:40 a.m., plus or minus four hours. This supported Nance Seifrit’s testimony. Dr. Coe’s graph would have placed Gail Dreher’s time of death at 11:00 a.m. and would have had a far smaller range of possible times for her expiration. Petitioner argues that admitting this testimony violated his constitutional right to a fair trial and his right to due process of law.
The District Court was clearly concerned about the admission of Dr. Tucker’s testimony, writing that “[e]ven under the liberal standards of the Federal Rules of Evidence, Dr. Tucker’s testimony should not have made it past the ‘gatekeeping *805role’ of the trial judge.” Dreher v. Pinchak, Slip Op. at 25 (quoting Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 597, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993)). The District Court was likewise alarmed that the trial court “permitted Dr. Tucker to present his findings, despite the fact that his method of applying the vitreous potassium test fails to satisfy” the traditional indicia of reliability. Id. Finally, the District Court opined that “[w]ere it a question of first impression for this Court to decide, the admission of this testimony might well be considered a violation of petitioner’s rights of due process.” Id. Then, after recognizing that “it is well established that due process may be violated by the admission of certain categories of unreliable and prejudicial evidence,” the District Court concluded that, “standing alone, the admission of Dr. Tucker’s testimony did not violate petitioner’s right to due process.” Dreher v. Pinchak, Slip Op. at 26, 27.
Accepting that the District Court’s concerns were valid, it was nonetheless error for the Court to consider the merits of this claim, because the record demonstrates that the alleged due process violation resulting from the admission of Dr. Tucker’s testimony was not “fairly presented” to the New Jersey state courts. To satisfy exhaustion, a petition must present every claim raised in the federal petition to each level of the state courts. Pi-card, 404 U.S. at 270, 92 S.Ct. 509 (1971). Specifically, a habeas petitioner’s state court pleadings must demonstrate that he or she has presented the legal theory and supporting facts asserted in the federal habeas petition in such a manner that the claims raised in the state courts are “substantially equivalent” to those asserted in the federal court. Doctor v. Walters, 96 F.3d 675, 678 (3d Cir.1996) (citing Bond v. Fulcomer, 864 F.2d 306, 309 (3d Cir.1989)).
The state court pleadings and briefs in this case demonstrate no such equivalency. Dreher’s brief to the New Jersey Appellate Division does discuss Dr. Tucker’s testimony. The issue, however, was framed entirely as one of state evidentiary law. Dreher’s brief states the issue thus: “The trial court erroneously permitted the state to elicit a purported expert opinion concerning time of death that was based on arbitrary and unscientific methodology.” Supplemental Joint Appendix at 49. The issue is presented as one of state evidentiary law. Furthermore, Dreher’s brief limits its discussion to the prejudicial effects of this testimony, without reference to federal law or reference to his rights to a “fair trial” or to “due process.” Dreher’s presentation and discussion of this issue in the state courts amount to a garden variety evidentiary issue and this is how the New Jersey courts reviewed it.2
We have noted, however, that there are ways in which habeas petitioners may communicate that they are asserting a federal claim without explicit references to the Constitution or federal statutes. In Evans v. Court of Common Pleas, Del. County, Pa., we held that the required constitutional message may be communicated through “(a) reliance on pertinent federal cases employing constitutional analysis, (b) reliance on state cases employing constitutional analysis in like fact situations, (c) assertion of the claim in terms so particular as to call to mind a specific right protected by the Constitution, and (d) allegation of a pattern of facts that are well within the mainstream of constitutional litigation.” 959 F.2d 1227, 1232 (3d Cir.1992) (quoting *806Daye v. Attorney General of New York, 696 F.2d 186, 194 (2d Cir.1982) (en banc)).
Even by these means, the Petitioner did not serve fair notice on the New Jersey courts that he was asserting a constitutional due process claim. Petitioner did not refer to a constitutional or federal right and only cited the state courts to New Jersey cases which considered New Jersey evidence law without employing any federal constitutional analysis. Dreher’s briefs to the New Jersey Appellate Division and to the New Jersey Supreme Court do not assert this claim in any terms “so particular as to call to mind a Constitutional right,” nor does his discussion of this claim “allege a pattern of facts well within the mainstream of Constitutional litigation.” The “fair trial” and “due process” claims he brings to federal court in connection with Dr. Tucker’s testimony are not exhausted because they were not fairly presented to the state courts.
V. Dismissal of a “Mixed Petition.”
As Dreher’s habeas petition now contains at least one unexhausted claim, it is a “mixed petition.”3 The Supreme Court has made clear that a section 2254 petition which includes unexhausted as well as exhausted claims, i.e., “a mixed petition,” must be dismissed without prejudice. Rose v. Lundy, 455 U.S. 509, 522, 102 S.Ct. 1198, 71 L.Ed.2d 379, (1982). Under the Antiterrorism Act, we may not grant a petition containing unexhausted claims except in a narrow range of special circumstances, not present here, or unless the State explicitly waives the exhaustion requirement, which it has not done in this case. See 28 U.S.C. § 2254(b). We therefore will remand the cause to the District Court with instructions for it to vacate its order and dismiss the petition for habeas corpus without prejudice.
. The exhaustion doctrine is something of a paradox. Its justifications—comity and judicial efficiency—primarily involve safeguarding the interests of courts. But, the fact that states may waive the exhaustion requirement necessarily means that, in operation, one party may determine whether a petition must be fully exhausted in the state courts (as well as the federal district courts).
. The Appellate Division decided this issue solely on state evidentiary precedent. See Dreher II, 695 A.2d at 698.
. Having found one unexhausted claim, we express no opinion as to whether all claims have been properly exhausted. We likewise express no opinion on the merits of Dreher’s petition.