Dissolving (or merging?) ALL intersecting line features

TS9

I'm trying to dissolve all adjacent line features in a single feature class, so I'd like to only have separate features if they are not intersecting any others in the same feature class. The way it's working right now is that line features are only being dissolved if they share an endpoint with exactly one other line feature, which isn't how I would expect Dissolve to work based on the description. I have the same problem whether Unsplit Lines is checked or not.

The attributes are not important to me. Is there a way to do this with Dissolve, or is Merge a better option?

Thanks!

TS9

I gave it a try, and that gives the same result as running a Dissolve with Create multipart features unchecked. There are still adjacent lines that aren't being merged.