ORDER AND AMENDED OPINION

ORDER

The opinion filed June 23, 2004, is amended as follows:

1. Slip Opinion page 8374, first full paragraph:

a. Line 1 — replace ‘Alex” with ‘Alan.”

b. Line 4 — insert a space between “ § ” and “245.”

2. Slip opinion page 8375, line 6, starting with “Further” — delete from this word to the end of the paragraph.

3. Slip Opinion page 8376, Section 2 subject line — replace “Appellant’s” with “Medina’s.”

4. Slip Opinion page 8377, line 3 — insert a comma between “away” and “when.”

5. Slip Opinion page 8378, last paragraph, line 1- — replace “specific” with “the relevant.”

6. Slip Opinion page 8379, subheading A — remove “A. AEDPA Standard of Review.”

7. Slip Opinion page 8380, second full paragraph:

a. Line 4 — replace “357” with “537.”

b. Line 9 — Replace the sentence starting with “The overwhelming majority ...” with “The overwhelming majority of trial errors are non-structural and do not trigger habeas relief unless the error resulted in ‘substantial and injurious effect or influence in determining the jury’s verdict[,]’ ” Brecht v. Abrahamson, 507 U.S. 619, 637 , 113 S.Ct. 1710 , 123 L.Ed.2d 353 (1993) (citation omitted), or unless the judge “is in grave doubt” about the harmlessness of the error. O’Neal v. McAninch, 513 U.S. 432, 436 , 115 S.Ct. 992 , 130 L.Ed.2d 947 (1995).

8. Slip Opinion page 8381 — lines 1 and 2 — place a period after “(9th Cir. 2002)” and remove “(internal citation omitted).”

9. Slip Opinion page 8381 through page 8383, section B — remove the entire section B.

10. Slip Opinion page 8384 — third full paragraph, line 3 — insert the following sentence after “(1983)” and before “The California Court”: “Under Chapman v. California, 386 U.S. 18, 24 , 87 S.Ct. 824 , 17 L.Ed.2d 705 (1967), habeas relief is not warranted if any constitutional error is found to be harmless beyond a reasonable doubt, or harmless under an equivalent state law standard.”

11. Slip Opinion page 8385 — Section IV — Remove everything in this section except the last paragraph that begins with “In this case,” and “AFFIRMED.”

With these amendments, the panel has voted to deny the petition for rehearing and to reject the suggestion for rehearing en banc filed on July 15, 2004.

OPINION

Alan Medina (Medina) appeals the district court’s denial of his habeas petition. Medina was convicted by a jury in California state court of assault with a deadly weapon (CaLPenal Code § 245(a)(1)) and felony hit-and-run ( Cal. Vehicle Code § 20001 ).

Medina’s habeas petition challenges certain allegedly prejudicial ex parte statements made by the trial judge to the jury in violation of his constitutional rights to counsel and to be present during trial. The California Court of Appeal found constitutional error but denied relief on harmless error grounds. We have jurisdiction pursuant to 28 U.S.C. § 2253 . Because the state court’s denial of Medina’s appeal was neither contrary to, nor an unreasonable application of, clearly established federal law, we affirm the district court’s denial of Medina’s habeas petition.

1. BACKGROUND

A. Factual Background

1. The Initial Meeting

This case deals with an instance of “road rage” in San Diego, California, at approximately ten o’clock in the evening. Medina was driving south on Fourth Avenue when he stopped at an intersection. To Medina’s immediate left were pedicab drivers Charles Ennion and Jimmy Hennessey, and their passengers.

After looking at Medina, Ennion either said, “Smile amigo,” or “Hey amigo, want to race?” Taking offense, Medina replied, “You don’t know me to be calling me amigo.” Though the parties disagree as to the order of these events, the record shows that Medina shone a spotlight onto Ennion, who moved his pedicab to block Medina’s movement. The pedicab passengers exited the cabs shortly thereafter.

At this point, the witnesses’ recollections diverge.

2. Medina’s Recollection of Events

Medina drove around Ennion’s pedicab, turned west, and stopped about four car lengths away. The pedicab drivers followed Medina, exited their cabs, and began arguing with Medina. Ultimately, the parties broke away, with Medina continuing westward.

While driving, Medina decided to make a U-turn, because he did not know whether the street he was on continued. Still “energized” after the confrontation with Enn-ion, Medina lost control of his car and ended up in the center divide facing northeast.

Medina paused briefly before moving to his right (eastward) in an arcing motion to return to the correct lane of traffic. Medina estimated that he was driving ten to fifteen miles per hour. At this point, Enn-ion started pedaling in Medina’s direction at “full tilt,” and made a sudden U-turn toward the left, causing Medina to unintentionally collide with Ennion’s pedicab.

Medina did not remember the pedicab going under his car. He reversed direction and started to drive away after Ennion began hitting the back of Medina’s car. Fearing for his safety, Medina fled the area.

3.The Pedicab Drivers’ Version of Events

After his passengers disembarked, Enn-ion parked his bicycle near the intersection, followed Medina on foot, and the two began arguing. At some point, Ennion decided that he was looking foolish and walked back to his pedicab. Once on his pedicab, Ennion began moving away, when he heard yelling and screeching tires, and saw Medina heading toward him head-on. Medina’s car hit the back wheel of Enn-ion’s pedicab and Ennion went under the car. Medina’s car traveled through two lanes of opposing traffic to strike Ennion.

Hennessey observed Medina make a U-turn, stop, and continue taunting Ennion. After Ennion got onto his bicycle and started moving, Medina “floored it,” striking Ennion. Medina continued pushing forward until Hennessy threw a hubcab at Medina, who then reversed direction and drove away.

4. The Passengers’ Observations

Two of Ennion’s passengers saw Medina cut across several lanes of traffic before colliding with Ennion. Another passenger saw Medina make a U-turn after passing Ennion. As Ennion began pedaling, the passenger observed Medina drive quickly toward Ennion. She also saw Medina’s car drag Ennion’s pedicab a short distance.

5. Other Witnesses’ Viewpoints

A bystander saw Medina drive down the street and then make an abrupt U-turn. Medina idled for about three minutes with his wheels turned “hard left” toward Enn-ion. After Ennion’s pedicab began moving, Medina accelerated and hit the front of Ennion’s pedicab. The bystander thought the collision looked intentional.

A driver in the vicinity recalled seeing Medina’s car, at a forty-five degree angle from the proper lane of traffic, striking a pedicab. The driver saw Medina’s car back up after the crash and strike the pedicab a second time before leaving. The driver recorded Medina’s license plate number and provided it to the police.

A resident of a second-floor apartment near the site of the incident heard yelling and tires screeching outside his apartment. When he looked out, he observed Medina’s car on top of a pedicab. Medina’s wheels were still spinning forward.

6. Testimony of Prior Assault Victim

The trial court admitted the testimony of a prior assault victim for the limited purpose of establishing Medina’s identity, and that the collision in the present case was not due to a mistake or accident. The prior victim testified that, two years earlier, she stopped her car on the side of the road to pick up a friend. Medina, who was behind the victim, became angry at the delay, got out and swung a shovel at the man she had stopped to pick up, and rammed the victim’s car.

7.Trial Court’s Response to the Jury’s Request for Clarification

While deliberating, the jury sent the trial judge a note that read:

The attorneys agreed that the judge should answer the note by re-reading the relevant jury instructions to the jury. The judge conducted the agreed-upon ex parte readback session, but prefaced that session with the following statement that was not agreed to by counsel:

The judge then provided citations to the relevant jury instructions.

B. Appellate History

Medina filed a direct appeal and a habe-as petition in the California Court of Appeal. The Court of Appeal decided that the ex parte statement resulted in constitutional error, but denied relief on the ground that the error was “harmless beyond a reasonable doubt.” The California Supreme Court summarily denied relief.

Medina then filed his federal habeas petition. The magistrate judge recommended denying the petition and the district court agreed. Medina timely appealed.

II. STANDARD OF REVIEW

We review de novo the district court’s denial of Medina’s habeas petition. Clark v. Murphy, 331 F.3d 1062, 1067 (9th Cir.2003). Because Medina filed his habe-as petition after the enactment of the Anti-terrorism and Effective Death Penalty Act of 1996 (“AEDPA”), his appeal is governed under the rules of that Act. Id. Under AEDPA, we may grant the petition only if the state court’s denial of relief:

(1) resulted in a decision that was either “contrary to,” or was an “unreasonable application” of, “clearly established federal law” as set forth by the United States Supreme Court; or

(2) was based on an “unreasonable determination” of the facts in light of the evidence presented in the State court proceeding.

28 U.S.C. § 2254 (d). Because the California Supreme Court summarily dismissed Medina’s habeas petition, we”look through” that dismissal and review the “last reasoned” state court decision. Bailey v. Rae, 339 F.3d 1107, 1112 (9th Cir.2003) (citation omitted). In the instant case, that decision is the one penned by the Court of Appeal.

The “contrary to” and “unreasonable application of’ clauses of § 2254(d)(1) provide independent avenues of relief. Clark, 331 F.3d at 1067 . The “contrary to” clause of § 2254(d)(1) provides relief if the state court “fail[ed] to apply the correct controlling authority, or if it applie[d] the controlling authority to a case involving facts materially indistinguishable from those in a controlling case, but nonetheless reaehe[d] a different result.” Id. (citation omitted). Under the “unreasonable application” clause of § 2254(d)(1), relief may be granted if the state court “identifie[d] the correct governing legal principle but unreasonably applied] that principle to the facts ...” Id. (citation and alteration omitted). Extraordinarily deferential to the state courts, the “unreasonable application” clause does not trigger habeas relief unless the state court’s analysis was “objectively unreasonable.” See id. at 1067-68. This requires a showing of error greater than clear error. See id. at 1068.

Finally, even if the state court’s decision was contrary to, or an unreasonable application of, clearly established federal law, habeas relief may still be denied absent a showing of prejudice. See Early v. Packer, 537 U.S. 3, 10-11 , 123 S.Ct. 362 , 154 L.Ed.2d 263 (2002) (per curiam). There are two forms of prejudice. Only a small group of “structural errors” are deemed so harmful that they warrant per se relief. Dyer v. Calderon, 151 F.3d 970 , 973 n. 2 (9th Cir.1998) (citing to Arizona v. Fulminante, 499 U.S. 279, 307-10 , 111 S.Ct. 1246 , 113 L.Ed.2d 302 (1991)). The overwhelming majority of trial errors are non-structural and do not trigger habeas relief unless the error resulted in “substantial and injurious effect or influence in determining the jury’s verdict[,]” Brecht v. Abrahamson, 507 U.S. 619, 637 , 113 S.Ct. 1710 , 123 L.Ed.2d 353 (1993) (citation omitted), or unless the judge “is in grave doubt” about the harmlessness of the error. O’Neal v. McAninch, 513 U.S. 432, 436 , 115 S.Ct. 992 , 130 L.Ed.2d 947 (1995). The relevant inquiry is whether the tainted evidence actually harmed the appellant. See Mancuso v. Olivarez, 292 F.3d 939, 950 (9th Cir.2002).

III. DISCUSSION

As described earlier, after the jury asked for clarification regarding the concepts of “proof,” “reasonable doubt,” and how to “take” sworn testimony, the parties agreed that the judge would re-read the relevant instructions to the jury outside the presence of the attorneys. Prior to the readback, the judge made the following prefatory statement:

The Court of Appeal determined that the trial court committed constitutional error by making those remarks, but disposed of that error on harmless error grounds.

Improper ex parte remarks made by the judge to the jury are subject to harmless error analysis. Rushen v. Spain, 464 U.S. 114, 118-20 , 104 S.Ct. 453 , 78 L.Ed.2d 267 (1983). Under Chapman v. California, 386 U.S. 18, 24 , 87 S.Ct. 824 , 17 L.Ed.2d 705 (1967), habeas relief is not warranted if any constitutional error is found to be harmless beyond a reasonable doubt, or harmless under an equivalent state law standard. The California Court of Appeal’s harmless error determination in this case was not “contrary to” established federal law. Although the Court of Appeal did not identify Chapman as the guiding point of its harmless error analysis, it applied a state-law “harmless beyond a reasonable doubt” standard that comports with federal law. See Chapman, 386 U.S. at 24 , 87 S.Ct. 824 ; see also Early, 537 U.S. at 8 , 123 S.Ct. 362 (noting that a state court need not cite Supreme Court cases, so long as its analysis is not contrary to governing caselaw). Neither did the decision conflict with any materially indistinguishable Supreme Court cases.

The Court of Appeal’s decision also did not amount to an “unreasonable application” of clearly established federal law. Medina argues that he was prejudiced because the trial judge’s impromptu instruction to the jury to “use your common sense and the common meaning of the words” provided the jurors with a “roving commission” to ignore the legal definitions contained in the jury instructions, and instead allowed jurors to interpret legal phrases ad hoc.

In rejecting Medina’s claim, the Court of Appeal took note of the fact that, after making his improper remarks, the judge expressly charged the jury with re-reading the relevant jury instructions. This command significantly reduced the likelihood that the jury applied a “roving commission” to ignore the governing legal definitions. See Weeks v. Angelone, 528 U.S. 225, 234 , 120 S.Ct. 727 , 145 L.Ed.2d 727 (2000) (holding that the Constitution requires no more when the trial court rereads the applicable instruction).

Medina also argued that the trial judge’s “rocket science” remark prejudiced him by marginalizing the jury. The Court of Appeal disagreed. After considering at length how the term “rocket science” is used in everyday life, the court concluded that the term did not denigrate the jury and that the phrase, being neutral as to Medina, was non-prejudicial.

While reasonable minds might disagree with the notion that the trial court’s terminology was non-derogatory, that disagreement hardly rises to the level of objective unreasonableness required by AEDPA. Moreover, even if the jury were insulted, we fully agree with the state court that the phrase was neutral as to Medina and that he suffered no prejudice thereby. It is just as likely that any insult benefited Medina as it is that it worked to his detriment.

Because the Court of Appeal’s approach to resolving Medina’s claim was consistent with the Supreme Court’s holding in Weeks , its application of the harmless error rule was not an objectively unreasonable application of federal law.

IV. CONCLUSION

In this case, the California Court of Appeal’s harmless error analysis was nei ther contrary to, nor an unreasonable application of, clearly established federal law. Accordingly, we AFFIRM the district court’s denial of habeas relief.

AFFIRMED.

. We have addressed Medina’s other arguments in a concurrently filed memorandum disposition. . A "pedicab” is a bicycle with a passenger compartment attached to the rear.