It's generally not the most advisable thing in the world, but super glue is great for awkward/deep/clean cuts. Especially if you're an American with poor healthcare.

Recently stabbed my hand quite deep in the muscle just below my index finger. Deep but clean, bled like hell and almost impossible to wrap. Just wash it clean, dry it as best you can and dab the outside closed, try not to get any in the cut itself. Works wonders, kept it neatly closed while I was sleeping and even managed to shower the next day without it opening up. After 24 hours it'll peel off pretty cleanly too (if you didn't go overboard). Let it air out for as long as you can to help it heal and only reapply when necessary. For me I just did two days, when it happened and the day after, and it was clean enough to heal closed a bit and only require light wrapping afterwards.

Not the first time I've done this and sure as shit won't be the last.