
806 A.2d 1232 (2002)
In re J.W.
C.S., Appellant.
No. 99-FS-843.
District of Columbia Court of Appeals.
Argued September 10, 2002.
Decided September 26, 2002.
Lauren S. Kahn, McLean, VA, appointed by the court, for appellant C.S.
*1233 Sheila Kaplan, Assistant Corporation Counsel, with whom Robert R. Rigsby, Corporation Counsel at the time, and Charles L. Reischel, Deputy Corporation Counsel, were on the brief, for appellee District of Columbia.
Before FARRELL, REID and GLICKMAN, Associate Judges.
GLICKMAN, Associate Judge:
This is an appeal from an order denying visitation. C.S. contends that the trial court abused its discretion in denying him the right to visit his putative son, J.W., without first holding an evidentiary hearing. C.S. also claims that the court erred in failing to grant him custody of J.W. We affirm the court's order.

I.
J.W. and his siblings were committed to the custody of the Department of Human Services in September 1996 after the court found them to be neglected in accordance with a stipulation signed by their mother. C.S. was not notified of the neglect proceeding and did not participate in it. Over two years later, at a review hearing in April 1999, C.S. appeared before the court for the first time and expressed a desire to "see what I can do to get custody of J.[W.] and take him under my care." C.S. represented that he had been living in New Orleans and had just learned that his children J.W. and C.W. (an older brother of J.W.) were in foster care. The court appointed an attorney to represent C.S. and directed Ms. Tracy Burton, the Child and Family Services social worker, to interview him and evaluate the situation. Stating that "a parent's interest in a child is welcome at any time," and that "it's always good to have ... as many resources as we possibly can," the court told C.S. that "we will look forward to having you ... at the remaining proceedings."
At the next review hearing, on May 28, 1999, C.S.'s counsel advised the court that C.S. "would like those children who are his with him," and "is interested in ... having some kind of supervised visits" with them. The court asked Ms. Burton if she had evaluated C.S.'s situation as a "possible placement." Ms. Burton reported that she had spoken with C.S. and his "paramour" on three occasions but still needed to schedule a home visit. The court approved C.S.'s request for visits with C.W. and then turned to the question of visitation with J.W. C.S.'s counsel reiterated that C.S. wished to visit J.W. and added that C.S. "would like to have J.[W.] placed with him." The court responded that it "ha[d] some difficulty with that last assertion," and cautioned counsel to "be careful about exactly what you are saying at this point in order to maintain credibility with the court." Nothing further was said about placing J.W. with C.S., but at his counsel's suggestion the court ordered C.S. to take a paternity test.
J.W.'s guardian ad litem, supported by his educational advocate and Ms. Burton, recommended against visits by C.S. for the time being. The guardian ad litem described J.W. as an "extremely emotional, fragile child" who could "barely handle what he's got right now," and opined that the reintroduction of his father into J.W.'s life would create a "major upheaval" at that time. The record does indicate that J.W. was struggling with severe emotional problems, and that he was just beginning to stabilize in school and at home. Noting that it had "been living with this case from the beginning," the court agreed that J.W.'s situation was "extremely precarious" and that it would not be in J.W.'s best interest to have visitation "right now." As the court commented later in the proceeding, J.W. "for [the] first time in a long time appears to be on an even keel and I'm going to keep him there for a while until *1234 I'm confident that visitation is not going to disrupt him. I have seen too many problems with the visitation." The court mentioned that J.W. would, for example, "dissolve and go to pieces" after visits with his mother. The court emphasized, however, that its denial of visitation was subject to reconsideration:
But, we can reassess and re-evaluate the situation. Ms. Burton is going to be meeting with Mr. S. You will have an opportunity to assess that home and we can then look at the next review time and see how things are going.
For his part, C.S. did not dispute that, given J.W.'s emotional frailty, visitation by C.S. would not be in his best interest at that time.
Nonetheless, following the May 28, 1999 review hearing, C.S. noted the instant appeal from the court's temporary denial of visitation. For whatever reason, that appeal has taken more than three years to come before us. The record does not disclose whether, in the interim, Ms. Burton performed the anticipated home visit or completed her evaluation of C.S. for placement purposes. Nor does the record disclose whether the court-ordered paternity test was performed, or, if so, what its results were. J.W. remains subject to the court's jurisdiction; there has been no termination of parental rights, though an adoption reportedly is being considered. We are informed that C.S. did not renew his requests for visitation and custody of J.W. at the several review hearings held in Superior Court after May 28, 1999. At oral argument, C.S.'s counsel advised that she has lost contact with her client.

II.
We have considerable doubt whether a live controversy is presented to us in this matter or whether C.S. is still interested in seeing or gaining custody of J.W. As we are not prepared to say that the appeal is moot, however, we address the claims that C.S. has asserted.
C.S.'s claim that the trial court erred in failing to grant him immediate custody of J.W. is not properly before us, because there is no final order or judgment on custody for this court to review. Under D.C.Code § 11-721(a) (2001), this court does not have jurisdiction to review issues "[s]o long as the matter remains open, unfinished or inconclusive," as it remained here. McDiarmid v. McDiarmid, 594 A.2d 79, 81 (D.C.1991). C.S. did not ask the court to award him immediate custody, and the court did not render a final ruling on that question. Rather, the suitability of placing J.W. with C.S. was still being investigated, seemingly with C.S.'s full cooperation. Although C.S. and his counsel expressed their desire for such a placement without undue delay, they acquiesced in the investigative process and did not seek an immediate decision on May 28, 1999. Nor, of course, did C.S. have an "absolute" right to be given immediate custody of J.W., whose previously adjudicated status as a neglected child C.S. did not dispute. See, e.g., In re Ko.W., 774 A.2d 296, 304 (D.C.2001) ("A parent's right to custody is not absolute. The court must act in the child's best interest and may not expose the child to serious risk of harm.") (citations omitted); D.C.Code § 16-2320(a) (2001). The trial court certainly did not abuse its discretion in deferring any custody decision pending the outcome of the investigation into C.S.'s suitability (not to mention the outcome of the paternity test ordered at the behest of C.S. himself).
We likewise are satisfied that the trial court did not abuse its discretion in denying C.S.'s request for visitation with J.W. for the time being. See Lewis v. Lewis, 637 A.2d 70, 72 (D.C.1994) (stating that court's ruling on visitation is subject to reversal only for "clear abuse of discretion"). *1235 Although a parent's right to visitation is "an important, natural and legal right," that right may be denied if it would be detrimental to the child's best interests. See In re M.D., 602 A.2d 109, 112 (D.C. 1992); D.C.Code § 16-2320(a). The trial court rested its decision to deny visitation temporarily on its well-grounded concern that J.W. was emotionally unstable and not ready to handle the intrusion into his life of his long-absent father. That decision was a reasonable one with a firm and undisputed factual predicate. See, e.g., Lewis, 637 A.2d at 72 (holding that visitation could be delayed until the child was psychologically prepared for it). We reject C.S.'s claim that the court should have held an evidentiary hearing before denying visitation. C.S. did not request an evidentiary hearing and therefore did not preserve this claim for appellate review. See Williams v. Gerstenfeld, 514 A.2d 1172, 1177 (D.C.1986). But even if the claim were properly before us, no evidentiary hearing was required becausein the absence of any question about J.W.'s emotionally fragile statethere was no material factual issue that needed to be resolved. Cf. In re Ko.W., 774 A.2d at 306 (holding that court abuses its discretion if it denies visitation without conducting an evidentiary hearing on a disputed issue of fact that is material to its decision).
For the foregoing reasons, we affirm the ruling on appeal.
So ordered.
