Is it possible that two-person plays, economically expedient for their small casts, are on the rise in L.A.? That they pose a challenge to hegemony of the 99-cents-only theater genre, the solo performance — a genre so often abused by critics for its penchant to either impersonate a celebrity or to indulge, as its name suggests, in autobiographical wanking?

If a pair of really good two-person plays running concurrently on the Westside is any indication, a mere couple of characters can get to the heart of just about anything with all the wit and vivacity of, say, a three-or-more-character play that would pose an exponentially greater challenge to cost-conscious producers.

In actuality, as in so many one-person shows, each of these pas de deux has many more characters than actors. The surplus just happens to reside offstage, referred to by the two actors. They are spouses or exes or children of the principals, employed without pay to flesh out the portrait of life embodied by the duo.

Sharr White's Annapurna, directed by Bart DeLorenzo, stars Megan Mullally (of Will & Grace fame) and her husband, Nick Offerman (of Parks and Recreation fame). For local stage observers, the teaming of DeLorenzo, Mullally and Offerman, as well as sound designer John Ballinger and costume designer Ann Closs-Farley, will bring back memories of performances at the Evidence Room, before DeLorenzo's 2009 departure and the appropriation of the venue by the staff of what's now Bootleg Theatre.

The action of Annapurna, first presented at San Francisco's Magic Theatre in 2011, unfolds in a mountain Colorado trailer home where poet Ulysses (Offerman) has gone to disappear, literally, from lung cancer. The play is a comedy.

Ulysses' ex-wife, Emma (Mullally), walked out 20 years ago after his appalling behavior (the primary plot mystery), which he was too drunk to recall. He remains clueless about what he did to drive her away. He just seethes that she disappeared with their 5-year-old son in tow.

So she suddenly shows up, unannounced — not surprising, since he has no phone, no Internet — with suitcases in hand, while he's naked (except for an apron and an oxygen tank) and while he's frying sausage either for himself or for his ratty dog, Jennifer, or for both.

The first few scenes have a staccato rhythm. The scenes eventually grow longer, their tug upon the audience being the sly peppering of revelations concerning what he did and what she did over the past 20 years, raising the questions of why she shows up at this particular moment and how two people who so obviously care for and about each other can sever a marriage and sustain an acrimony lasting decades.

There's a formula at play in which their initially bristling manner with each other dissolves into a tentative dance, something approaching 19th-century romanticism, love and death — the stuff of so many operas by Rossini and Puccini and Verdi, but here played out in miniature with punchline jokes and comedic reactions.

Offerman's performance redefines “crusty” — the bearded mountain man living on food stamps amidst dog shit and strewn remnants of a handwritten poem he's been working on for the better part of 20 years. He's an educated man who speaks in colloquialisms. Nothing puffed up about this poet. Thomas A. Walsh's hyper-realistic set slices his trailer home laterally so that the entire thing is parked on the stage, with one side cut away, in order for the audience to peek in like voyeurs. There hasn't been an abode so trashed up since David Mauer and Hazel Kuang's living-room set of a hoarder in Rogue Machine's production of Rob Mersola's Dirty Filthy Love Story last year. In Annapurna's set, the dirt has been ground into what's left of the carpet.

This is the filth Emma starts to clean up, in her attempt to repair her ex-husband for reasons only she can disclose. Let's just say her actions are maternal, aiding a once-violent ex-spouse she now describes as “harmless.” Mullally, with her squeaky voice and her slightly exasperated deportment, muscles her way through, as though reeling from a cocktail of tenacity, disbelief, weariness and love. Because this is, in the end, a love story with a pulse and a poeticism strong enough to prevail over its minor contrivances.

Like Annapurna, Allen Barton's gorgeous new play, Years to the Day, is a reunion. It too concerns two friends, here in their early 40s (Michael Yavnieli and Jeff LeBeau), wrestling with each other over their histories. It too lasts 90 minutes without intermission. It too swims against an undercurrent of death. It too has beautifully tender performances. It too hangs dramaturgically on the question of who did what to whom and why.

In my opinion, it's a better play, for a number of reasons. There's no cutting off scenes for comic effect. It just has two guys get together for coffee. They haven't seen each other in person for four years. From that oh-so-simple premise it rolls along, without scene changes, without sound effects and with barely a set — a table and two chairs. Director Joel Polis has such confidence in the brains residing in Barton's play, in the vivacity and veracity of the conversation, that he leaves his duo sitting for most of it.

Thus unfolds a social satire in the style of My Dinner With Andre that's simply George Bernard Shaw for the 21st century.

The pair chide each other, they banter over hanging onto an Android phone with last year's tech in order to pounce next year on the newer model. They argue over a movie, one of them infuriating the other because he liked it, the other becoming lunatic-inflamed that each scene was merely a hallucination. And this series of hallucinations is actually the story of their lives and their marriages and children and their sojourns through life on the brink of death.

Their discussions of politics, of culture, of technology, abstracted by their setting in a netherworld maybe five years in the future, is a gentle parody of the way we discuss politics, or culture, or technology. They talk about “the event” — and argue over security measures that followed. One becomes so exasperated with the other that he breaks out in hives. The play is a slightly absurdist, slightly whimsical, deeply ironic and very funny commentary that deflates all we might take to be important, and self-important.

One reveals he's gay. It's not a melodramatic moment at all. The confession is an irritated response to the other character's spew opposing gay marriage. The offender confuses Stonehenge with Stonewall — or pretends to. The play is The Odd Couple with substantive repartee.

The only production flaw is that no couple would argue this loudly in a public place and not be asked to leave, or respond to the annoyance of passers-by. It could easily be set in a private place.

It's so good to see a play unafraid of articulating an argument, because plays now are supposed to be all about subtext. Years to the Day is about its text, about life crises and self-absorption and desperate, comic loneliness. It's a very smart play, an hour and a half of delight.

ANNAPURNA | By Sharr White | Odyssey Theatre Ensemble, 2055 S. Sepulveda Blvd., W.L.A. | Wed.-Sat., 8 p.m.; Sun., 2 p.m. (no perfs May 24-26); through June 9 | (310) 477-2055 |

YEARS TO THE DAY | By Allen Barton | Skylight Theatre at the Beverly Hills Playhouse, 254 S. Robertson Blvd., Beverly Hills | Fri.-Sat., 8 p.m.; Sun., 7 p.m.; through May 12 |

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