If you like that, watch Undeclared, from the same people. Also cancelled after one season.
I like bingeing TV shows with a relatively small number of episodes because it seems like less of an investment to watch the whole series. Detroiters and Detectorists were mentioned above, but here are some of my other favourites:
Delocated (Adult Swim, 30 episodes): A TV network creates a reality show about an idiot in Witness Protection who is being hunted by the Russian mob. The short first season (where he is being hunted by an equally inept Russian gangster) was funny, but the second season is possibly my favourite season of any TV series, ever. A great combination of black comedy and silly comedy.
Enlightened (HBO, 18 episodes): A corporate executive comes back from rehab eager to make improvements to her life but she has a tough time of it when she gets demoted to doing data entry in a sub-basement. Laura Dern does an amazing job making you want to root for a flawed character.
Cock’d Gunns (IFC Canada, 13 episodes): An inept rock band tries to make it big in this semi-improvised series. It’s kind of like “Anvil! The Story of Anvil” with a touch of “Flight of the Conchords”. Some catchy songs, too.
The Comeback (HBO, 2 episodes): Lisa Kudrow is great in this sad and funny mockumentary about a has-been actress who gets a second chance after getting a role in a (terrible) sitcom. The second season was made 9 years after the first season. A real labour of love.
Dirk Gently’s Holistic Detective Agency (BBC America, 18 episodes): The TV show inspired by Douglas Adams’s book is not necessarily a faithful adaptation, but it’s charming and funny in its own right.
(part 2 of my list will come later)
Fawlty Towers - John Cleese of Monty Python runs a small hotel, wackiness ensues. Only 12 episodes.
Firefly - Probably everyone interested in this has seen it, but it’s a terrific space western that only lasted one season. Great cast, great dialog, great plots for the most part.
Life - Damien Lewis plays a LA cop who was framed for the murder of the family who lived next door to him, and went to prison for a long time before being exonerated. He sues and wins a lot of money and his old job back. Sarah Shahi is teamed up with him as his partner. She is an ex-addict being given another chance at being a cop, and she is expected to keep an eye on him. Damien’s character has to acclimate to life outside prison, solve murders, and in his free time tries to figure out who framed him and why. Only 2 seasons but has a fairly satisfying conclusion.
Another former HBO series; Rome, with 22 episodes over two seasons. Really good and a lot of fun to watch. I was really sorry when it ended sooner than planned (although they crammed a lot into the ending). HBO has a lot of series, some of which lasted a while but a lot of which were short. I liked The No. 1 Ladies’ Detective Agency, particularly for the Botswana setting.
And from another premium cable network, Counterpart, twenty episodes over two seasons. A spy drama with a really unusual twist.
Great show but definitely not NICE 
Moone Boy - a kid in Ireland and his imaginary friend negotiate growing up in a small village.
Gravity Falls - Animated series about a brother and sister spending their summer solving supernatural mysteries that are haunting them at their Uncle’s tourist trap shop. Arguably a well known show, but it had a very short run and tends to get overshadowed by other similar fantasy animation like Adventure Time or Steven Universe. There is also a new show just started with a similar tone and some crossover of creators called The Owl House.
Blunt Talk - Patrick Stewart is a talk-show anchor alongside an eclectic bunch of ne’er-do-wells who help run the show.
The Trip - Comedians Rob Brydon and Steve Coogan play fictionalised versions of themselves as they travel around, ostensibly reviewing hotels and restaurants, but really having mid-life crises and celebrity impression competitions.
No Activity - Two cops sit in a car during a stakeout and have inane conversations while nothing happens during their watch. Meanwhile just out of their line of sight, lots of things are happening. There are two versions, the original Australian one and the US adaptation. Some big names associated with it too.
Zapped - An ordinary boring man finds himself transported to a magical fantasy kingdom which is a lot less enchanting than he anticipated.
The Lost Room - six-episode mystery/adventure involving a bizarre motel room and historical artifacts that provide supernatural powers, excellent acting and story
Patriot on Amazon Prime is one of my favorite shows. Just two seasons (it looks like it got cancelled afterwards). A perfect mix of heavy drama, whimsical but dark humor, and fantastic characters.
I’m a little torn about the cancellation. On the one hand, I’d love to see more. On the other hand, I do think there is a benefit to “quitting while you’re ahead” and having the entirety of the production be very good.
Great idea for a thread, by the way. It’s captured quite a lot of suggestions I want to follow up on.
Not to be that guy (okay, to be that guy) OP said “let’s try to keep recommendations at shows that have been on in the past 5 years or so.”
More of my favourites.
Wrecked (TBS, 30 episodes): A group of misfits is trapped on a desert island after a plane crash. It starts as a parody of “Lost” but later it adds elements from other sources (like “The Most Dangerous Game”).
Nobodies (TV Land, 20 episodes): Hugh Davidson, Larry Dorf and Rachel Ramras (comedy writers on “Mike Tyson Mysteries” and other shows) write and star in this fictionalized account of how they tried (and failed) to pitch a movie idea to Melissa McCarthy through their acquaintance with her husband Ben Falcone. In Season 2, they get sucked into writing a (lousy) sitcom instead. Talk about meta.
Corporate (Comedy Central, 20 episodes + renewed for one more season): Two junior executives deal with working at a soulless conglomerate. Kind of like “Better Off Ted”, but with even more black comedy. Lance Reddick from “The Wire” is hilarious as the amoral CEO.
Ugly Americans (Comedy Central, 31 episodes): A cartoon about a (human) social worker who runs a support group for new immigrants in a version of New York City teeming with monsters.
Jeff and Some Aliens (Comedy Central, 10 episodes): Three aliens have the job of observing “Earth’s most average guy” and their attempts to help him invariably make his life worse. (Kind of like the episodes of “Rick & Morty” where Rick’s inventions make life worse for the family.) I thought this show was very funny and I think the premise would have been good for at least one more season.
Burning Love (E!, 42 12-minute episodes): A spoof of “The Bachelor/ette” with a Murderers’ Row of great comedic actors playing the contestants.
Hunderby (Sky, 10 episodes): Julia Davis’s follow-up to her deliciously evil sitcom “Nighty Night”. It’s a whacked-out pastiche of “Jane Eyre” and “Wuthering Heights”, with dialogue that is equal parts effete and raunchy.
I’ve mentioned On My Block in other threads. At 28 episodes (8 of which were released today) and a fourth season not ruled out, it is pusing the limit of small, but it is good.
Also:
The animated Kipo and the Age of Wonderbeasts (at one season of 10 episodes so far.)
Stan Against Evil (3 seasons, 24 episodes.)
Happy! (2 seasons, 18 episodes.)
We’re currently watching Basketson Hulu. Zach Galifinakis stars as twins Chip and Dale Baskets, with Louis Anderson absolutely knocking it out of the park as their mother, Christine Baskets. Chip flunked out of French clown college and has to get his life back together back home in Bakersfield, CA. It sounds positively fucking bizarre when I type it out and read it, and it is, but in a really, really good way.
Four seasons, 10 episodes each season. Highly recommend.
People of Earth - (TBS, canceled) Starring Wyatt Cenac as a guy who joins a support group for people who have been abducted by aliens. Turns out the aliens are real! But everyone is not quite sure. This isn’t a rip-roaring comedy but it’s a…nice little show.
Another Period - (Comedy Central, canceled) Created by and starring Natasha Leggero and Riki Lindhome. Stars your typical bunch of Comedy Central regulars like Michael Ian Black, David Koechner, Brett Gelman. It’s kind of a take off on Downton Abbey & The Kardashians, set in Rhode Island at the turn of the 20th century. About an absurdly rich family and their bratty girls and their weird husbands. And even weirder staff.
Good suggestions, everyone! I’ve already found some of these and started watching. Since they’re so “little” I can binge them pretty quick!
I don’t know if you’ve seen Mum, but it’s become a favorite of mine. I know it’s not a “little” show in the UK, but I found it on our PBS station, and then watched the last season when I had a free trial of Britbox. It has a grand total of 18 episodes.
I immediately thought of those two, and two others, both involving time travel:
Journeyman, 2007 – Kevin McKidd, star of Rome, as a journalist who involuntarily slips back and forth in time. Lasted only one season.
New Amsterdam, 2008 – Nikolaj Coster-Waldau, aka Jamie Lannister, as an immortal cop living and working in modern NYC. Not really time travel, but he has a lot of flashbacks. Like every show I like, lasted only one season.
And if you like it, you will probably like Highlander, which lasted several seasons, and was much better than the movies. Also about an immortal with a lot of flashbacks.
Is Marcella good?
I Am Not OK With This is a fun little show on Netflix, adapted from the same writer who did The End of the Fcking World*. Kind of like if that show were combined with Stranger Things. Oddly, it stars not one but two of the juvenile cast members of It.
Afterlife with Ricky Gervais–one season and I hear there will be a second (on Netflix).
Also Catastrophe with Rob Delany and Sharon Horgan - American guy in London on business has a one-week stand with a Brit who gets pregnant. He returns and they stay a couple. Very realistic depiction of a modern relationship. Really well written with other interesting and quirky character (on Amazon).
**Modern Love **on Netflix is a series of stand-alone episodes about relationships.
You want little? I give you Little Lunch. The Office style mockumentary, but with Australian 5th graders at recess. Deals with hard-hitting issues like:
[ul]
[li]misplacing one’s glasses[/li][li]sharing of the monkey bars[/li][li]disgusting lunches from home[/li][/ul]
Available on Netflix. Only 26 episodes (and only 15 minutes long) and 2 30 minute specials.