In an infamous and oft-quoted “secret” speech to his SS troopers, Heinrich Himmler predicted that the world would someday be grateful for the crimes they committed against Europe’s Jews, and that the important thing was for the SS to be remembered for remaining “decent” despite the provocations those people presented. For a long time, it has been unclear whether that rhetorical flourish was provoked by a need to bolster the flagging enthusiasm of his minions, to lie to himself about the nature of their actions and his orders, or the psychological mechanism of “splitting” that made it possible for Himmler and his troops to continue their lethal work without suffering an incapacitating psychological breakdown.

A new documentary, “The Decent One,” directed by Israeli filmmaker Vanessa Lapa, doesn’t give a definitive answer to the question, but drawing on a rediscovered cache of family papers, photos, diaries and letters, it is highly suggestive. Lapa’s father purchased the material, which had been hidden in Tel Aviv, and she constructed a propulsive 96-minute film that traces the SS chief’s rise to power and his family life through his own words and images from the period.

Perhaps unsurprisingly, the portrait of Himmler that emerges is of a dedicated anti-Semite and fervent follower of Adolf Hitler. He also appears to have been a doting father to his only daughter, a scold to his adopted son, and a once-loyal then errant husband who fathered two more children by a younger mistress while still married to a wife seven years his senior. He turns out to be the kind of man who can demand that the “wealth we have taken from the Jews” be turned to the public good while sending elaborate presents to his own family, including a fur coat for his wife and a gold bracelet for his daughter.

In short, Himmler comes out of “The Decent One” as someone who is either self-deluded, a hypocrite or a not terribly interesting conman. But there is the matter of six million murdered Jews, which is always bubbling just below the surface of Lapa’s film. While wallowing in self-pity, Himmler sticks doggedly to his grim task. Lapa structures her film cleverly, engaging with her audience’s foreknowledge while letting the Himmler family’s ordinariness horror give the demonic spin. It’s a hard film to watch, and a hard one from which to look away.

“The Decent One” opens on Oct. 1 at Film Forum (209 W. Houston St.).