I've seen lots of examples on others' blogs of "messy" wire-wrapping. Here's an example, by someone far more competent than me. It looks deceptively easy (sigh). But it's a lot harder, in the same way that playing jazz- piano is a lot harder than a nice regular bit of Haydn.
I decided to experiment with a similar technique for my new pair of earrings, using 0.4mm silver-plated wire. I think I can say, with fairness, that the results were mixed. It does kind-of work, but not if you look too closely, especially with a Macro lens :-D
It might have gone better with thicker wire - but I wanted the earrings to be delicate and pretty, not all chonky-like.
Clearly, further practice is required!