Interested in seeing a show this month? Hoping for one that will force you to contemplate the consequences of infidelity and the temporal nature of life, plus be entertaining to boot? Then you have two choices, and you can’t go wrong.

Both The Mountaintop and The Last Five Years are two-person shows about how fame affects relationships, with tangents involving how caffeine fuels the writing process. Since one is a musical about a fictional writer and the other is a drama that opens with Martin Luther King Jr. struggling to write a speech, the comparisons should probably stop there.

On Broadway in 2011, The Mountaintop starred Samuel L. Jackson as the Civil Rights leader and Angela Bassett as the room-service maid who brings him up coffee and sticks around for foreplay and cigarettes. Without the celebrities, and with age-appropriate actors (King was just 39 when he was assassinated), it’s a different show. Actually three different shows, given the structural shifts in Katori Hall’s well-written—-but not entirely well-made—-play. This Arena Stage production is largely convincing audiences to go along with its unconventional premises, thanks to two outstanding performers spouting dialogue not entirely appropriate for a man of the cloth.

Historical plays that meditate on American issues of race seem to be en vogue. There’s one, Mary T. and Lizzie K., playing just across the hallway at Arena Stage, while another, All the Way, about Lyndon Johnson’s fight to pass the Civil Rights Act, won the Harold and Mimi Steinberg/American Theatre Critics Association New Play Award this month. What’s gutsy about The Mountaintop is that it’s more rooted in Hall’s imagination than the the history books, and not interested in lionizing its main character. When the show opens, King (a slightly pompous but always earnest Bowman Wright) is nervously pacing the outer balcony of a cheap motel, calling down to friend who’s supposed to head out in the pouring rain to pick him up a pack of Pall Malls.

Then the set rotates, revealing the interior of a drab room with pink chintz bed covers, and the man who led the March on Washington heads into the bathroom to take a piss. He comes out, calls home, tries to write a speech again, then calls for coffee.

Enter Joaquina Kalukango as the maid, Camae. “Room service, sir.” she says. “That was fast,” he responds. “Well,” she continues, “I been called quickie Camae befo’.”

Somehow, Kalukango manages to come off as vivacious but not overly come-hither. She’s just a pretty, bright Memphis girl with strong opinions. When she dons his suit coat and shoes and suggests revision to King’s speech, you’ll fall for her just as he does. But as great a chemistry as these two actors have, the will-they-or-won’t-they wordplay only carries the play so far. Via sound effects and projections that border on Twilight Zone-cheesy, the play takes a leap and changes genres. King has a premonition that his end is nigh. Innuendo is replaced by more esoteric humor. (The St. Augustine joke is funny, but the audience at the matinee I attended never laughed harder then when King gasped at the thought of being replaced by Jesse Jackson Jr.) Just when things start to sober up, there are more sound effects and another stage rotation. With help from a scrim curtain and a slide show, the two characters muse on the future of Civil Rights movement. Kalukango delivers a rapid-fire monologue recapping 50 years of history like a slam poet teaching social studies. It’s an upbeat way to end a show, especially since everyone knows the main character is about to get shot. But the transitions and effects feel slightly cheap, like Hall relied on theatrical sleight-of-hand rather than her own writing. So one hopes that, like King and his unfinished speeches, this young dramatist has many more plays up her sleeve.

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If The Mountaintop is about going out on a high, then The Last Five Years is about starting out at rock bottom. There may not be a harder opening number in all of musical theater then “Still Hurting,” the break-up ballad that opens this two-person musical. So many shows begin with big happy toe-tapper. In this musical, it’s just Erin Weaver, lolling on a bed in a schlumpy chenille sweater, bemoaning the end of her marriage.

Weaver, you may recall, is the actress who charmed Washington audiences as the angelic roller-skating muse last year in Signature’s production of Xanadu. She doesn’t do sadness very well, and it’s not an insult to say that from the opening number on, her performance in The Last Five Years only gets better. So does life for her character.

In Jason Robert Brown’s brilliant, nonlinear musical, Weaver plays Cathy, a struggling actress who sings her way through a five-year relationship in reverse. Weaver alternates songs with leading man James Gardiner, who is nebbishly adorable as Jamie, an MFA student whose first novel is the biggest thing Random House has published since Bright Lights, Big City. The two characters’ storylines meet in the middle for one duet that can be staged as a wedding scene, but in this production it’s more of an engagement, followed by a subtler exchange of “I do’s.”

After a try-out in Chicago, The Last Five Years became an off-Broadway cult classic, and gave a significant career boost to stars Sherie Rene Scott and Norbert Leo Butz. Last month, Anna Kendrick and Jeremy Jordan signed on to star in a film adaptation. But Signature’s production proves the show will work if you have two excellent actors, a smart director, and a great six-piece orchestra playing Brown’s eclectic score.

You do need an audience with an urbane sense of humor. Gardiner nails his opener, “Shiksa Goddess,” the ballad of the rogue Hebrew-school graduate who finally dates a gentile after trying out “every Shapiro in Washington Heights.” But even if you haven’t dated a Jewish novelist, there are plenty of universal relationship questions to ponder. When is “just having coffee” not just having coffee? When do you stop supporting your partner’s struggling career, and suggest a career change?

Jamie and Cathy don’t need a relationship counselor, just an audience in need of a little of a little musical theater therapy. So longtime lovers and supportive girlfriends should buy tickets, grab a tissue, and settle in to spend 90 minutes on Signature’s couch. If you’re on a first date, try The Mountaintop.

The Mountaintop runs through May 12 at Arena Stage. The Last Five Years runs through April 28 at Signature Theatre.