When I used to think of Heinrich Himmler — and it wasn’t often that I conjured the chief overseer of Nazi concentration camps — the image of a meek man humming old blues songs and skipping didn’t come to mind.

Brendan McNally changed all that with his debut novel, “Germania,” a whimsical piece of historical fiction that re-envisions the often-neglected and short-lived period in Nazi history after Hitler’s death, known as the Flensburg era.

The novel is centered loosely on a Jewish family who, prior to World War II, performed in a cabaret act called the Flying Magical Loerber Brothers. As celebrities, the four brothers manage to use their fame to escape Hitler’s persecution. They hide within the crumbling Nazi bureaucracy rather than suffer the fate of most German Jews of the time.

Ziggy Loerber mans a U-boat, working alongside infamous Nazi naval officer Capt. Peter-Erich Cremer. Ziggy’s brother Manni works as an undercover spy and earpiece for chief Nazi architect Albert Speer. Franzi becomes Himmler’s masseuse and confidant. Sebastian, the only Zionist of the bunch, orchestrates terrorist plots against the Nazis and dreams of escaping to Israel.

As the story unfolds, the brothers display an uncanny ability to influence top Nazi officials. Throughout the novel they are front and center during the most significant events in the toppling of the Flensburg regime — from the capture and interrogation of Speer, to the death of U-boat captain Wolfgang Lüth. Manni juggles with Speer, and Franzi massages Himmler’s ulcer — zany encounters that also have historical significance in the world posited by “Germania.”

McNally imagines intimate conversations taking place between the brothers and the German officials during these moments that often seem to humanize the war’s worst offenders.

In one scene, McNally relates how Speer “dreamed of polar bears and seeing the sun rise over ice flows, [feeling that] for once his debts to Adolf Hitler’s memory were forgiven.”

The novel’s fictionalization of the fall of the Third Reich is a unique and ambitious undertaking. McNally, formerly a defense journalist for the Pentagon, has done a great deal of investigation of the Flensburg era, and he weaves the plot of the novel artfully into its historical context. World War II history enthusiasts will likely enjoy the author’s colorful rendition of events, in the same way that Watergate buffs can appreciate the various film spoofs the incident has inspired, such as the 1999 movie “Dick.”

While the novel’s premise is entertaining, the portrayals of the Loerber brothers are shallow. Although the brothers clearly are conflicted about being Jewish Nazi cohorts, their feelings are tread on lightly and never fully explored. Toward the end of the book, all qualms the brothers have with the Nazis seem to disappear unresolved.

This is a peril of writing satire, putting diversions before depth.

Also, McNally seems to want to incorporate nearly every major Third Reich figure into his novel. This comes at the expense of developing the central characters’ motives.

But what is most worrisome about “Germania” is that it ends on an unsettlingly sympathetic note for Speer, Karl Dönitz — the German naval commander who led the Flensburg government — and their fellow war conspirators. It’s a baffling decision, since McNally elected to tell the story through four Jewish brothers.

Despite these missteps, McNally certainly piqued my interest in a part of World War II I had never considered. He has accomplished a feat most first-time novelists wouldn’t dare — rewriting a very sensitive period of history with flair and an uninhibited imagination.

The Flying Magical Loerber Brothers pranced through my dreams for several days after I turned the last page. And that is an acrobatic act worthy of praise.

“Germania” by Brendan McNally (384 pages, Simon and Schuster, $26)