Holocaust deniers are infinitely more shameful but just as loony as card-carrying members of the Flat Earth Society or delusional fringe types still maintaining NASA faked the moon landing on a soundstage.

It seems offensively absurd a respected author and professor of Jewish history would have to go to court to prove the Holocaust happened — but that’s just what happened to Deborah Lipstadt, who was sued by an infamous Holocaust denier who claimed HIS reputation had been ruined because Lipstadt’s book identified him as anti-Semitic, a Hitler sympathizer and a Nazi Party apologist.

That trial is the centerpiece of “Denial,” a powerful but often stilted drama bolstered by two great performances from accomplished actors and nearly sunk by an unfortunately (and surprisingly) off-key performance from another fine actor.

Let’s start with the misfire first. The normally wonderful Rachel Weisz pierces the eardrums with a shaky and flat performance as Deborah Lipstadt. Her “New York” accent is so thick it wouldn’t fly in a “Saturday Night Live” skit.

Rachel Weisz as Deborah Lipstadt in "Denial." | BLEECKER STREET MEDIA

Rachel Weisz as Deborah Lipstadt in “Denial.” | BLEECKER STREET MEDIA

Onward. In the mid-1990s, Deborah is living a busy life as a Holocaust studies professor at Emory University in Atlanta. An accomplished author, Deborah is giving a talk about her latest book, “Denying the Holocaust,” to a packed house when the British historian and well-known Holocaust denier/showboat David Irving (Timothy Spall) loudly interrupts her, quoting passages from her own book about him and waving $1,000 over his head, offering it as reward to anyone who can prove beyond a shadow of a doubt the Holocaust actually occurred.

It gets worse. Irving sues Deborah and her publisher, Penguin Books, claiming Deborah’s passages about him in “Denying the Holocaust” have destroyed his reputation and have prevented him from making a living.

Under British libel laws, the onus is on Deborah to prove her statements about Irving are true — that Irving is racist, Irving is anti-Semitic, Irving willfully distorted the historical record and Irving knows the Holocaust occurred but has deliberately lied about it for decades.

For such an accomplished, learned person, Deborah seems flustered and at times flies off the handle when she learns about the workings of the British legal system. She swoons in the presence of the solicitor Anthony Julius (Andrew Scott), a handsome charmer who represented Princess Diana in her divorce case — but she’s dumbfounded when she learns Anthony will only prepare her case, and the barrister Richard Rampton (Tom Wilkinson) will actually represent her in court.

Also, the defense strategy is for Deborah not to testify. And for that matter, they won’t be calling any Holocaust survivors to the stand either. While I’ll leave the reasoning behind these decisions unexplained so as not to give too much away, suffice to say the absence of the heroine and of the real victims of Irving’s hateful crusade from key courtroom scenes makes for relatively muted trial fireworks.

Wilkinson gives the most complete performance in the film as Rampton, who refuses to get too emotionally involved, even during a visit to Auschwitz to gather evidence. Always the proper Brit, Rampton is quick to offer red wine in plastic cups and small sandwiches to guests in his office, but he always seems preoccupied with the details of the case because he IS always preoccupied with the details of the case.

Timothy Spall is a snaggletoothed snake charmer as David Irving. Irving is an appalling human being and he is on the wrong side of history in a way that should shame his descendants for generations, but the man is not a fool, and he is dangerous because there are some who are all too willing to believe his supposedly well-researched garbage. Spall does a magnificent job of portraying an obsessed and slick con artist who at his core is a monster in a tailored suit.

As directed by Mick Jackson (“The Bodyguard,” “Volcano”) and scripted by David Hare (“The Hours,” “The Reader”), “Denial” is so stagey at times we half-expect the actors to step into a spotlight and address us directly.

Despite the drawbacks, the power of the story shines through.

★★★

Bleecker Street Media presents a film directed by Mick Jackson and written by David Hare, based on the book “Denial: Holocaust History on Trial” by Deborah E. Lipstadt. Rated PG-13 (for thematic material and brief strong language). Running time: 110 minutes. Opens Friday at local theaters.