Short short stories are usually a couple of pages long. Hoshi Shinichi is famous for his short short stories but there are other collections as well. They are good if you need a quick translation project, or have a short time and want to finish a whole story.
Do you worry about finding interesting stories that are also a good reading level for you? Don't worry. In 2013 we created the "Read Japanese" collection in the East Asian Reference room on the 22nd floor. There you will find picture books, graded readers, short short stories, and separate work by authors that are appropriate for students with a reading level of a middle school students or less.
Many of these stories are actually "leveled" so that you can progress by reading grade 3, grade 4, up through middle school.
Take a look at 齋藤孝のイッキによめる!名作選 EA Ref Room Read Japanese PL537 .S346
There is also a series called 集団読書テキスト, where short stories are published as stand-alone texts. No pretty illustrations, but at least this way you don't have to worry about having your book recalled because someone else wants it. These are all in the Read Japanese collection, shelved by the author's name rather than the set.
Do you like horror? How about Neil Gaimanesque stories? Try the Kaidan ehon series.
Would you rather read manga than literature? How about trying literature adapted into manga? Look for the 文芸まんがシリーズ.
Some of you might like to try a light novel (ラノベ). See 文学少女 or read about real people in fictional settings like the 名探偵 series.
Would you rather browse than search? Try this link to see what is in the Read Japanese collection. If you want a smaller list to choose from, here is a link to short story collections in Read Japanese.
Here you will find anthologies of short stories that are centered around a particular theme or type of writer. These have been chosen because they are easier to read for language learners and in many cases have been compiled for Japanese junior high school students.