You need to be very sparse when writing short stories. Whereas a novel needs to answer every* reasonable* question or a reader gets frustrated, a short story needs to leave a lot more up to the reader's imagination. Not only that, you need to pick a small enough objective that you can achieve it in the word count. This is true of every story you'll ever write no matter the length.
On to the best answer I have found to your question, though it is in many ways a starting point and you may still have to take the butcher's cleaver to your sentences when you're done.
I always find this helpful as a good estimate before I write a story or as a diagnosis tool afterwards. Plus, math speaks to me.
Story Length [words] = ((Characters + Locations) * 750) * 1.5 * MiceQuotients
The mice quotient is basically "big ideas" that you can plan a story around, that also tend to guide how long a story will be since (as you've noted) there's always explaining to do around them. Most of these are self describing, but below I've used Lord of the Rings (lotr) to provide examples.
MILIEU: A milieu story concerns the world surrounding the characters you create.
To further expound, it's generally having to do with the entering/exiting of a place. IE, LOTR: Leave the shire, come back to the shire. Enter Moria/Leave Moria.
IDEA: An idea story concerns the information you intend the reader to uncover or learn as they read your story.
Some LOTR ideas: Power Corrupts, Industrialism vs Agrarian Society, War is Hell,
What is a Hero
CHARACTER: A character story concerns the nature of at least one of the characters in your story. Specifically, what this character does and why they do it.
Some LOTR characters: The fellowship (9) + bilbo + the important elves + the important dwarves + the important humans + the named evil wizards + all those side characters + + + omg its too many, but it is finite.
EVENT: An event story concerns what happens and why it happens.
LOTR examples: The party, the hobbits have to leave the shire, sauroman turns evil & Gandalf must survive this, We tried, but can't cross the mountain pass, how do we survive a Balrog, why hobots shouldn't drop buckets down wells.
Once you have written a work, you need to isolate what that work is about and trim down. It's ok if you overshoot on a first draft by 10%-40% of the length. It's better if you do. But, you'll need to figure out what your good bits do and work on compression & removal to get down to the element of what you want. This usually involves scanning sentences for redundant or useless turns of phrase; quirks of voice which expand the length and are unneeded; or elements which do not serve to achieve your desired effect. This section is only included here to say, if you end up above your estimated length, it's an indicator that you can still cut and that your plan should involve some amount of this until you've written long enough (10+ years professionally) that you start to incorporate the lessons you've learned from revision into your at-keyboard-drafting-process.