
532 So.2d 75 (1988)
Alberto GUERRERO, Appellant,
v.
The STATE of Florida, Appellee.
No. 86-2654.
District Court of Appeal of Florida, Third District.
October 18, 1988.
*76 Bennett H. Brummer, Public Defender, and Elliot H. Scherker, Asst. Public Defender, for appellant.
Robert A. Butterworth, Atty. Gen., and Michelle Crawford, Asst. Atty. Gen., for appellee.
Before SCHWARTZ, C.J., and HUBBART and BASKIN, JJ.
BASKIN, Judge.
Alberto Guerrero appeals his conviction and sentence for second-degree grand theft of a car. We reverse.
After observing Guerrero driving a car shown by a computer check to have been stolen the previous day, the officer stopped the car and arrested Guerrero. Prior to the trial, the trial court precluded Guerrero from questioning the arresting officer during the trial about exculpatory statements he made to the officer. At trial, on direct examination, Officer Perez described Guerrero's arrest and the officer's statements to Guerrero at the time of the arrest. During cross-examination, the officer testified that when he stopped the car, the keys were in the ignition; the car had not been "trashed," repainted, or hot-wired; the defendant gave his name but did not have a license; and Guerrero was polite and cooperative. Limited by the court's ruling, Guerrero's attorney could only proffer that the officer would have testified that Guerrero had explained his possession of the car. He was not permitted to elicit testimony that Guerrero told the officer a girlfriend had given him the car and that he didn't know it was stolen. Over defendant's objection, the court instructed the jury that an inference of guilt arises from unexplained possession of recently stolen property. See § 812.022(2), Fla. Stat. (1985). During deliberations, the court acceded to the jury's request and reread the instruction. The jury returned a guilty verdict, and the court entered judgment.
Guerrero claims that the trial court erred in precluding cross-examination of officer Perez concerning the explanation Guerrero gave at the time of his arrest. As a general rule, a defendant's out-of-court self-serving exculpatory statements are inadmissible hearsay. Moore v. State, 530 So.2d 61 (defendant's self-serving exculpatory statements are inadmissible hearsay), on rehearing (Fla. 1st DCA Aug. 31, 1988); Fagan v. State, 425 So.2d 214 (Fla. 4th DCA 1983) (officer's testimony of defendant's exculpatory statements at time of arrest is inadmissible hearsay); Watkins v. State, 342 So.2d 1057 (Fla. 1st DCA) (same), cert. denied, 353 So.2d 680 (Fla. 1977). See also Logan v. State, 511 So.2d 442, 443 (Fla. 5th DCA 1987) (defendant's self-serving statements made over four hours after crime are inadmissible hearsay); however, where the state has "opened the door" by eliciting testimony as to part of the conversation, defendant is entitled to cross-examine the witness about other relevant statements made during the conversation. See Morey v. State, 72 Fla. 45, 72 So. 490, 493 (1916) (where state offered defendant's inculpatory statement, trial court erred in preventing defendant cross-examining the witness about exculpatory statements made in same conversation; "[t]he state having opened the door by proving a part of the conversation, it cannot close it upon the defendant so that he cannot offer the other part of the conversation which relates to the same subject matter."); West v. State, 53 Fla. 77, 43 So. 445, 446 (1907) ("Evidence of self-serving declarations and conduct ... when they form no part of the conduct or conversations introduced by the prosecution, should not, as a rule, be admitted in a criminal prosecution... ."); Ackerman v. State, 372 So.2d 215 (Fla. 1st DCA 1979) (Smith, J. specially concurring) (where state witness testifies to defendant's incriminating statements, accused is entitled to have remainder of conversation admitted even though favorable); Burch v. State, *77 360 So.2d 462 (Fla. 3d DCA 1978) (defendant's self-serving statements admissible where part of conversation entered into evidence). Cf. Delap v. State, 440 So.2d 1242, 1247 (Fla. 1983) (trial court properly overruled defendant's objection where defendant sought to elicit testimony from witness which would aid him in having confession suppressed, while blocking prosecution's inquiries which were not beneficial to his cause), cert. denied, 467 U.S. 1264, 104 S.Ct. 3559, 82 L.Ed.2d 860 (1984). See generally, C. Ehrhardt, Florida Evidence, § 108.1 (2d Ed. 1984); 7 Wigmore, Evidence, § 2113 (Chadbourne Rev. 1978).
Recognizing that Guerrero's exculpatory statement retains its hearsay character, see Sundale Assocs., Ltd. v. Southeast Bank, 471 So.2d 100, 103, n. 5 (Fla. 3d DCA 1985), we hold that the potential for unfairness mandates the admission of Guerrero's statement. The doctrine of curative admissibility "rests upon the necessity of removing prejudice in the interest of fairness.... and [i]ntroduction of otherwise inadmissible evidence under the shield of this doctrine is permitted only to the extent necessary to remove any unfair prejudice which might otherwise have ensued from the original evidence." United States v. Winston, 447 F.2d 1236, 1240 (D.C. Cir.1971); see United States v. Castro, 813 F.2d 571, 575-577 (2d Cir.), cert. denied, ___ U.S. ___, 108 S.Ct. 137, 98 L.Ed.2d 94 (1987); see also United States v. Sutton, 801 F.2d 1346, 1368 (D.C. Cir.1986); Mulford v. State, 416 So.2d 1199, 1201 (Fla. 4th DCA 1982) (decision suggests, but does not decide, that fairness may require admission of inadmissible segment of letter); see generally United States v. Pendas-Martinez, 845 F.2d 938, 944 (11th Cir.1988); C. Ehrhardt, Florida Evidence, § 108.1 at 29 (2d Ed. 1984). Here, the officer testified as to part of the conversation that occurred during Guerrero's arrest, namely, that he told Guerrero that the car was stolen and he was under arrest. He testified that Guerrero told him his name and that Guerrero was polite and cooperative, but he omitted Guerrero's explanation. That explanation was within the scope of direct examination[1] and was clearly relevant to the only issue at trial  Guerrero's unexplained possession of recently stolen property. The exclusion of segments of the conversation gave the jury the misleading impression that Guerrero had not offered an explanation for his possession of the car. We therefore hold that the trial court erred in excluding the explanation.
Clearly, the error cannot be considered harmless. Defendant's unexplained possession of the car was the key issue. The absence of an explanation and the broken door lock were the only record evidence in support of his conviction. Furthermore, in its closing argument, the state argued that defendant's unexplained possession of the car gave rise to an inference that he knew it was stolen, further misleading the jury. The court's instruction on this inference prompted the jury to infer that the defendant knew or should have known that the property was stolen, and virtually directed the jury to convict. State v. Young, 217 So.2d 567 (Fla. 1968); State v. Grimmage, 522 So.2d 523 (Fla. 2d DCA 1988). The court even reread the instruction at the jury's request. The repeated emphasis on defendant's unexplained possession of the car precludes a finding that the error complained of did not contribute to the verdict. See Ciccarelli v. State, 531 So.2d 129 (Fla. 1988); State v. DiGuilio, 491 So.2d 1129 (Fla. 1986); Johnson v. State, 388 So.2d 1088 (Fla. 3d DCA *78 1980). Cf. Nelson v. State, 362 So.2d 1017 (Fla. 3d DCA 1978) (where jury questions and juror's statement conclusively show jury drew adverse inferences from absence of explanation significantly influencing verdict, exclusion of testimony is not harmless error).
REVERSED AND REMANDED.
NOTES
[1]  "[W]hen the direct examination opens a general subject, the cross-examination may go into any phase, and may not be restricted to mere parts which constitute a unity, or to the specific facts developed by the direct examination. Cross-examination should always be allowed relative to the details of an event or transaction a portion only of which has been testified to on direct examination. As has been stated, cross-examination is not confined to the identical details testified to in chief, but extends to its entire subject matter, and to all matters that may modify, supplement, contradict, rebut or make clearer the facts testified to in chief by the witness on cross-examination." Roberts v. State, 510 So.2d 885, 893 (Fla. 1987) (quoting Coco v. State, 62 So.2d 892, 895 (Fla. 1953)), cert. denied, ___ U.S. ___, 108 S.Ct. 1123, 99 L.Ed.2d 284 (1988).
