The defendant, Scott Weeks, was convicted of operating a vehicle after having been certified an habitual offender, see RSA 262:23 (1993), after a jury trial in Superior Court (Dickson, J.). On appeal, he argues that the trial court erred in limiting his cross-examination of a key prosecution witness. We affirm.
On January 9, 1986, the defendant was found to be an habitual offender and his driver’s license was revoked. The order was served on the defendant personally that day, and a confirmation notice was sent by the department of safety to the defendant the next day, advising him that his license was revoked for a minimum of four years and until reinstated. The notice was not returned as undeliverable.
On August 22,1992, the defendant was arrested and charged with knowingly operating a motor vehicle after having been declared an habitual offender. Contested at the defendant’s trial was the issue of whether he knew he was an habitual offender at the time he was arrested. To prove the defendant’s knowledge, the State presented *465the evidence of the 1986 notifications to the defendant, in hand and by mail, of his habitual offender status. The State also offered the testimony of Lynda St. Amor, the defendant’s former girlfriend. St. Amor had lived with the defendant for five and a half years beginning in early 1988, during which time they frequently argued about his habitual offender status when he would drive her car. During the summer of 1992, several weeks before the defendant’s arrest, St. Amor called the department of motor vehicles to find out how the defendant could become decertified. She related to the defendant what she had learned, and he indicated that he understood.
After the defendant’s arrest, according to St. Amor, he asked her to lie for him by corroborating his story that he did not realize he was still an habitual offender at the time he was arrested. After the two ended their relationship, St. Amor contacted the county attorney, informing him that the defendant was aware of his habitual offender status.
On cross-examination, defense counsel sought to impeach St. Amor’s testimony by exploring her bias against the defendant, which derived, according to the defense theory, from his having ended their relationship several months earlier. St. Amor testified on cross-examination that she had been actively involved in securing legal representation for the defendant when he was first charged and even complained about the performance of his first attorney. When St. Amor stated that she had been troubled by the defendant’s asking her to lie for him, defense counsel asked her if she would ever lie for money, followed by the question, “Was it you who were convicted in the Dover District Court of welfare fraud?”
The prosecutor objected on the grounds that the defendant had violated New Hampshire Rule of Evidence 609 and Superior Court Rule 68 in failing to provide notice of his intention to use a prior conviction for impeachment. A chambers conference was immediately held. The following day the court ruled that the defense had violated both rules but found that the violations were not intentional. “[Cjoncerned with the rights of this defendant to confront his accusers” and with the fact that “the credibility of this witness is an important issue in this trial,” the trial court ruled that the witness could answer the question but ordered “that there be no further cross-examination in that area unless the witness denies the conviction.” The court further ruled that, in order to offset the State’s disadvantage at having been deprived of the opportunity to elicit the conviction during direct examination, the State would be allowed to inquire into the circumstances surrounding the plea and *466conviction on redirect. The court expressly reserved ruling on whether the defense would then be permitted further cross-examination on the matter.
When the trial resumed, the trial court directed St. Amor to answer the last question posed, i.e., whether she was convicted in Dover District Court of welfare fraud. She answered:
Yes, I was. It was back in — five years ago. I was working. I had stopped working because my daughter was abused by a baby-sitter. She spent five days in the hospital. I went on welfare because at that time I didn’t trust any baby-sitters. The child support was coming directly to me. After I got my first check, right before I got my second one, I went and I reported it to my case worker that I was getting child support, and at that time we made an agreement that I would pay back the money. Within a couple of days after I reported it and signed an agreement that I’d pay it back I was arrested, but the money was paid back. And it was only a few hundred dollars.
At an ensuing bench conference, defense counsel asked to be permitted to question St. Amor regarding the amount of money involved, her agreement to plead guilty in exchange for the State’s dropping a second charge, and the purposeful mental state underlying the conviction. Citing its earlier ruling, the trial court refused to allow further cross-examination regarding the conviction.
The defendant argues that the trial court violated his State and federal constitutional rights to confrontation and abused its discretion by limiting cross-examination of St. Amor on her prior conviction. The State counters as a threshold matter that the constitutional claim is not preserved, and we agree.
On appeal, the defendant’s challenge is to the trial court’s refusal to permit further cross-examination of the witness on the subject of her conviction once she had admitted it. The record is plain that the defendant raised a constitutional argument before the trial court only in an effort to persuade the judge to allow into evidence the conviction itself. The trial judge, ruling to admit the conviction, stated he was doing so because he was “concerned with the rights of this defendant to confront his accusers.” The defendant’s asserted constitutional argument having thus been addressed and acceded to by the court, and the witness having admitted the conviction, the defendant received all the protection to which he had asserted the constitution entitled him.
Now the defendant contends that the trial court improperly foreclosed further inquiry of the witness beyond the fact of the *467conviction. No constitutional basis for this argument was advanced at trial when the situation arose. We will not consider constitutional arguments not made in the first instance in the trial court. State v. Stratton, 132 N.H. 451, 456, 567 A.2d 986, 989 (1989). Accordingly, we decline to reach the defendant’s arguments grounded in the confrontation clause and apply an abuse of discretion standard. See State v. Isaacson, 129 N.H. 438, 439-40, 529 A.2d 923, 924 (1987).
Trial courts have broad discretion in determining the scope of cross-examination. State v. Gooden, 133 N.H. 674, 677, 582 A.2d 607, 609 (1990). In making this determination, the trial court must balance the probative value of the proffered testimony against its prejudice, State v. Brown, 132 N.H. 520, 525, 567 A.2d 544, 547 (1989), as well as the likelihood of confusion and delay generated by the evidence. Isaacson, 129 N.H. at 440, 529 A.2d at 924.
Here, the trial judge permitted the defendant, despite counsel’s violation of Superior Court Rule 68, to inquire about the witness’s conviction. See State v. Niquette, 122 N.H. 870, 872-73, 451 A.2d 1292, 1293 (1982) (holding that exclusion of conviction evidence was within court’s discretion when Rule 68 was violated by defendant’s failure to demonstrate convicted individual had or waived counsel). The witness admitted she had been convicted of welfare fraud, a crime that on its face conveys her dishonesty. In her testimony, she described the defendant’s offense as one committed deliberately, not accidentally as the defendant contends.
The defendant argues that he should have been permitted to question St. Amor about the precise amount of money involved, where she testified that it was “only a few hundred dollars” but the actual amount was over seven hundred dollars. According to the defendant, the witness’s purported misrepresentation of her conviction opened the door to further inquiry. See State v. Norgren, 136 N.H. 399, 401-02, 616 A.2d 505, 507 (1992). He also asserts that the trial court refused to allow him to make an offer of proof and failed to engage in a balancing of probative worth and prejudice. Contrary to this assertion, however, the record indicates that the trial court had been apprised in chambers of the offense and had seen a copy of the criminal complaint underlying the conviction. The trial court was thus in possession of the information the defendant sought to proffer, and an offer of proof was not necessary.
Moreover, the trial court had made clear its intention not to have “a trial within a trial” on the subject of the witness’s conviction. At the same time, the court demonstrated solicitude to the defendant’s interest in impeaching the witness’s credibility in the face of defense counsel’s violation of Rule 68. We find that the trial court exercised its sound discretion in balancing the interests on both sides.
*468The defendant’s argument that the witness opened the door to further cross-examination is unpersuasive. For the opening-the-door doctrine to apply, the testimony at issue must have created a misimpression. See Norgren, 136 N.H. at 401-02, 616 A.2d at 507. We do not believe that the jury was materially misled by the alleged understatement of the amount involved in the crime. The witness admitted to having cheated the State out of a “few hundred dollars.” That the actual amount may have been over seven hundred dollars does not change the essential nature of the fraudulent conduct she admitted in front of the jury.
Finally, we find no basis for the defendant’s contention that the witness opened the door to inquiry about the purposeful natqre of the offense and about the fact that she had originally been charged with two counts of welfare fraud but convicted of only one pursuant to a plea bargain. We do not read the witness’s testimony regarding her conviction as disclaiming her purposefulness in committing the unlawful conduct. Nor does her testimony contain any reference to the original charge or whether she negotiated a plea agreement. As there was no misleading advantage to rebut, the door was not opened to further cross-examination on the subject.
Although the defendant was not permitted to elicit specific details underlying the witness’s conviction, he was able to show that she had committed a crime involving dishonesty, which is strong impeachment evidence and an ample basis for discrediting the witness before the jury. Any additional information would have had relatively little probative value and could have led to the “trial within a trial” that the trial judge expressly sought to avoid. Limiting the cross-examination in this area was well within the trial court’s sound discretion.
Affirmed.
BRODERICK, J., did not sit; BATCHELDER, J., retired, sat by special assignment under RSA 490:3; all who sat concurred.