Soldering question: how to reliably solder thin stranded copper wires together?

I've been struggling with soldering some very small stranded copper wires together. The wires are very high gauge (seems like 26awg) and there's maybe only 10 or so thin strands. After stripping the wires and attempting to twist them together, and try to solder them. However, I can't twist them together tightly enough for a good joint. And the wires end up with a sizeable gap in the twists that gets filled in with solder. It works, but it makes this huge lump in the wire and I imagine it's not a very strong joint either.

I have some of those "heat shrink with some low temp solder in them" butt connectors on the way, but I feel like there has to be a better technique. Can you provide some great ideas?