The defendant, Elizabeth Winn, appeals the Superior Court’s (Perkins, J.) denial of her motions to suppress evidence and to immunize a defense witness. The defendant argues that the government’s delay in applying for a search warrant after seizing evidence violated her rights under part I, article 19 of the New Hampshire Constitution and the fourth amendment to the United States Constitution. The defendant also asserts that the trial court’s refusal to compel the State to grant immunity to a defense witness infringed upon her State and federal due process rights. We affirm.
The defendant was convicted of conspiracy to possess marijuana with the intent to sell. See RSA 318-B:2, I (1995); RSA 629:3, I (1996). The defendant’s co-conspirators were Paul Blackmer and Jorge Flores. The events leading up to the defendant’s arrest and conviction are as follows. On Friday, April 1,1994, Flores mailed two packages containing marijuana to the defendant’s minor children through a private courier service in California. The courier service’s proprietor noticed various characteristics about both the package and Flores that matched those highlighted by a drug package profile provided by the United States Drug Enforcement Administration (DEA). Consequently, the proprietor isolated the two packages and contacted the DEA. Shortly thereafter, two law enforcement officers arrived and allowed a narcotics detection dog to “sniff search” Flores’ packages. The dog detected the presence of narcotics. One of the officers took possession of the packages, secured them at the local DEA evidence locker for the weekend, and obtained a search warrant on Monday, April 4, 1994.
I. Delay in Applying for Search Warrant
The defendant first argues that the trial court improperly denied her motion to suppress because of the government’s delay in applying for a search warrant. The record below shows that the defendant did not present this specific constitutional objection to the trial court. “It is well settled in this State that this court will not consider grounds of objections not specified or called to the court’s attention at the trial.” State v. Cassell, 129 N.H. 22, 24, 523 A.2d 40, 41 (1986). Though the State discussed the reasonableness of the delay in its objection to the defendant’s motion to suppress, and the trial court mentioned the issue in its order, the defendant neither specifically objected to the delay in obtaining a search warrant nor adduced sufficient facts from which the trial court could properly resolve the issue. Consequently, we decline to consider this issue on appeal. See State v. Stearns, 130 N.H. 475, 486, 547 A.2d 672, 678 (1988).
*814 II. Defense Witness Immunity
The defendant next argues that the trial court’s refusal to compel the State to request use immunity for Paul Blackmer, a defense witness, under RSA 516:34 (Supp. 1996), violated her due process rights under the State and Federal Constitutions. At the suppression hearing, the parties stipulated that Blackmer, with whom the defendant had an intimate relationship, would refuse to answer any questions and that his testimony would incriminate him. As a result, the defendant urged the trial court to compel the State to grant Blackmer immunity. Following the trial court’s denial of the defendant’s motion to immunize Blackmer, the defendant filed a motion to reconsider, raising new factual allegations concerning Blackmer’s anticipated testimony. The trial court denied the motion. Because the defendant asserted no reason why she had previously failed to raise the new factual allegations in her original motion to suppress, the trial court correctly declined to consider them. See Super. Ct. R. 59-A; Brown v. John Hancock Mut. Life Ins. Co., 131 N.H. 485, 492, 558 A.2d 822, 826 (1989). We do the same.
The defendant’s notice of appeal invokes the defendant’s “due process right to present all proofs favorable to her defense.” See N.H. Const. pt. I, art. 15. Neither the State constitutional right to present all proofs favorable nor the Federal Constitution’s compulsory process clause, however, encompasses the right to compel the State to request immunity for a defense witness. State v. Roy, 140 N.H. 478, 482, 668 A.2d 41, 44 (1995). The defendant’s pleadings and arguments before the trial court intertwined a due process claim with an assertion of the right to present all favorable proofs. In light of our decision in Roy, we will examine only the defendant’s due process claim.
We analyze the defendant’s due process claim under our State Constitution, State v. Seymour, 140 N.H. 736, 742, 673 A.2d 786, 791, cert. denied, 117 S. Ct. 146-47 (1996), and reference federal case law only to aid in our analysis. See Roy, 140 N.H. at 480, 668 A.2d at 43. Because the Federal Constitution provides the defendant no greater protection, we decline to engage in a separate federal analysis. Id.; cf. Blissett v. Lefevre, 924 F.2d 434, 441-42 (2d Cir.), cert. denied, 502 U.S. 852 (1991).
Criminal defendants do not have a constitutional right to immunity for defense witnesses who exercise their fifth amendment privileges against self-incrimination. See State v. Farrow, 118 N.H. 296, 305-06, 386 A.2d 808, 814 (1978). “It is true that under narrow circumstances where the defendant shows that the testimony sought *815would be directly exculpatory or would present a highly material variance from the tenor of the State’s evidence, failure to immunize a witness may have due process implications.” Roy, 140 N.H. at 481, 668 A.2d at 44 (quotation and citation omitted; emphasis added). Pursuant to these standards, the defendant must first demonstrate that the witness’s testimony would be directly exculpatory or present a highly material variance from the State’s case. State v. Monsalve, 133 N.H. 268, 270, 574 A.2d 1384, 1385 (1990). If the defendant demonstrates that his or her case falls within these narrow circumstances, we then decide whether, on the facts of the defendant’s case, the executive branch’s refusal to immunize a defense witness denied thp defendant a fair trial. See Roy, 140 N.H. at 481, 668 A.2d at 44; cf. Blissett, 924 F.2d at 442 (federal standard for compelling grant of immunity includes a showing that: (1) the testimony is material, exculpatory, and not cumulative; (2) the defendant cannot obtain the evidence from other sources; and (3) the prosecutor has engaged in overreaching or granting immunity in a discriminatory manner to gain a tactical advantage). Our standard reduces the possibility of cooperative perjury between defendants and their defense witnesses and ensures that the judiciary will not lightly interfere with prosecutorial decisions including whom to prosecute and what evidence to present at trial. See also Blissett, 924 F.2d 434.
The defendant, however, has not satisfied this initial burden; therefore, we need not consider whether she was denied due process based on the facts of this case. In the defendant’s motion to immunize Blackmer, she proffered the conclusory assertion that the “[testimony by Mr. Blackmer would be directly exculpatory and would present a highly material variance from the tenor of the State’s evidence.” In her motion to authorize Blackmer’s deposition, as opposed to her motion to immunize, the defendant asserted that “Mr. Blackmer is expected to testify that Ms. Winn was not involved in the conspiracy with him.”
A review of the record reveals that the defendant’s “offers of proof” at the motion hearing also failed to provide essential facts sufficient to satisfy her burden. Among other conclusory assertions, the defendant stated that Blackmer’s “testimony would be at . . . [a] highly material variance to the State’s information,” and would present “favorable evidence that applies directly to the theory of the defense . . . [and] evidence to impeach Rebecca Boulerisse,” a State witness expected to testify under a grant of immunity. Additionally, the defendant speculated as to the substance of Blackmer’s testimony, which she alleged could be used as both *816directly exculpatory and impeachment evidence, stating: “I think Paul Blackmer can certainly testify ... as to how he got together with Rebecca Boulerisse, how they became involved in whatever their involvement was, and how Elizabeth Winn had nothing to do with that.”
The trial court interpreted the defendant’s conclusory assertions and the defendant’s own explanation of her relationship with Blackmer to mean that Blackmer would testify “that while the defendant may have been aware of Blackmer’s actions, or had her suspicions about them, she did not participate in any of Blackmer’s alleged activities,” and that Blackmer would testify “that he did not want the defendant involved because she was interfering in his business.” The trial court denied the defendant’s motion for immunity, reasoning that Blackmer’s anticipated testimony was reconcilable with the State’s evidence and could even lend support to the State’s case. The court reasoned that “the fact that the defendant may have been aware of Blackmer’s activities and that the defendant was interfering in them may also be interpreted as lending further support in favor of the State’s case.”
We affirm the trial court’s determination that the defendant made an insufficient showing that Blackmer’s testimony would be directly exculpatory or at a highly material variance to the State’s evidence. Considering the anticipated testimony as found by the trial court — that the defendant was aware of, and interfered with, Blackmer’s activities — the testimony is not at a high material variance to the State’s evidence because the testimony is reconcilable with the State’s version of events. Specifically, this testimony may be interpreted as drawing the defendant into the conspiracy because the defendant knew of the drug activities and to some extent was entangled in them. This is particularly true when the proffered evidence is viewed in light of the defendant’s inculpatory admissions. See State v. MacManus, 130 N.H. 256, 259, 536 A.2d 203, 205 (1987). We note, moreover, that the trial court made efforts to ameliorate the denial of immunity to Blackmer by granting, with the State’s consent, the defendant’s motion in limine to preclude Boulerisse from testifying on several issues. Cf. id. at 259-60, 563 A.2d at 205 (noting the trial court’s and State’s efforts concerning the exclusion of evidence to assure defendant a fair trial).
The defendant also sought Blackmer’s testimony to impeach Boulerisse. The record reflects that there were sufficient alternative means to impeach Boulerisse through cross-examination about her various inconsistent statements regarding the defendant’s involvement with Blackmer’s drug endeavors. Cf. Roy, 140 N.H. at 482, 668 *817A.2d at 44 (recognizing the importance of cross-examination in casting doubt on credibility). We therefore conclude that the trial court did not err in denying the defendant’s motion to immunize Blackmer.
Affirmed.
All concurred.