The streaming service Mubi operates more like a repertory cinema than any of its peers: A new movie is introduced to its subscribers every day, and it’s available on the site for the theatrical equivalent of a limited run. After 30 days, it’s gone.

Speaking as a user, I consider it an interesting, compelling and sometimes maddening strategy. Recently, while browsing the site’s “Now Showing” page, I spotted a Russian science-fiction film from 2011, “Target,” directed by Alexander Zeldovich. I saw a screening of it a couple of years ago and have wanted to revisit it ever since. The left-hand corner of the screen read “6 Days Left.” (It’s off the site now, as you read this.) There’s something about that ticking clock that produces anxiety.

On the other hand, the diversity and the quality of the selections are exhilarating. Mubi is one of several first-rate sites that cater to cinephiles, and its mix of current and vintage films, the global scope of the selections, and the truly eclectic array of genres is great. (There are films from Australia, Russia, Japan, South Korea, Portugal, Israel, Italy and Britain as I write, and none from Senegal, Mali and Morocco, but there have been, and I’m sure there will be others.) You could watch one movie a day and never feel aesthetically pigeonholed.

Mubi started about 10 years ago under the name the Auteurs. It ran a small number of films and had a feisty editorial section called (then and now) the Notebook, which I know a bit about because I was one of its early regular contributors. Its social network component was vibrant, but its identity as a film provider in those early days struck me as a little murky. The site was founded by Efe Cakarel, a voluble entrepreneur who, in a recent phone conversation, described the process that led to Mubi’s way of doing things. “In the beginning, we wanted to be like Netflix, but the unit economies of an ‘all-you-can-eat’ site is very capital intensive,” Mr. Cakarel said. “The question becomes, how do you create a compelling experience? If you can’t get 10,000 titles, how about a limited selection?”