Dallas Tolentino and Jen Rabbitt Ring in “A Bid to Save the World” at Rorschach Theatre. (Ryan Maxwell Photography)

We can deduce one thing about Death, the waggish but menacing figure who turns up in the new play “A Bid to Save the World”: He can’t be suffering from a vitamin C deficiency. In the Underworld imagined by dramatist Erin Bregman, each human existence eventually manifests itself as an orange; when a given life span ends, Death peels the fruit and eats it.

The image is both whimsical and pleasingly mythic. And, in Rorschach Theatre’s premiere production of the play, actor Dallas Tolentino (in unnerving facial makeup) makes Death a splendidly sinister and moody presence. Unfortunately, the character turns up in only one of the three stories that twine through Bregman’s quirky meditation on loss and mortality. Acting that is merely serviceable saps zest from a second, sci-fi-flavored plotline, and a third registers as dull and trifling in its critical early moments. All three stories ultimately connect in an ingenious way, but, at least as directed by Lee Liebeskind, the play as a whole often feels slow and studied.

Still, you have to admire Bregman’s determination to explore, in a fresh and offbeat way, the great mystery that is death. Almost as striking as her notion of a citrus-based eschatology is the tale of Adam (Robert Pike) and Evelyn (Linda Bard), two high school students who live in a world where no one ever dies. When the kids decide to do a class report on that oldfangled kicking-the-bucket thing, they visit their local library, where they get help from a brooding librarian (Jen Rabbitt Ring).

The research sequences play out in a dark comic vein: Actors in hoodies channel the library’s reference sources, miming causes of mortality, from the all-too-familiar (cancer) to the unusual (lightning strikes). Adam and Evelyn watch, fascinated.

The acting in this segment of “A Bid to Save the World” isn’t always as polished as it could be. In a more realistic section — about Sister (Tyasia Velines), who mourns fiercely after her Brother (Christian Sullivan) has gone to an orange-rind-bedecked Hades — the pace lags more than is warranted even in an evocation of the disruptive ordeal that is grief.

A stylized story line about two sisters (Natalie Cutcher and Daven Ralston) who disagree about their home’s noise level is tedious initially, with a contextualizing big reveal turning up only in the play’s final moments.

While toggling between these scenarios, the production incorporates evocative music. Of particular note, the ensemble periodically chimes in on songs that vary in style, from gospel to rock to sea shanty. (The ensemble devised the songs and other music. “A Bid to Save the World” was developed locally, at the Inkwell and the Source Festival.)

These interesting sonic elements are matched by a compelling use of space: In the Atlas Performing Arts Center’s Sprenger Theatre, the play unfurls on three stage areas that connect like spokes on a wheel, with the audience between the spokes. One’s eye is particularly drawn to the area where an autumnal trellis invites thoughts of the mythological figure Persephone. This is where Death hangs out. When he’s not peeling oranges, by the way, he seems to be turning the rinds into sculpture.

A Bid to Save the World, by Erin Bregman. Directed by Lee Liebeskind; costumes, Danielle Preston; props, Becky Mezzanotte; sound, Veronica J. Lancaster; lighting, Katie McCreary; music director, Hilary Morrow. $20-$30. Through Oct. 2 at Atlas Performing Arts Center, 1333 H St. NE. ­202-399-7993. atlasarts.org or rorschachtheatre.com.