I really would like to know if sticky end ligation could potentially be performed with very high efficiency, and which factors influence that. However, I can't find any papers on the subject, even though I'm sure they exist. I was hoping someone would know of some literature.
The best resource for troubleshooting ligations I found (and use frequently) is this NEB page. That is assuming you've already referred to the instructions provided with the enzyme you're using. In my case it's T4 Ligase, again from NEB. It's helpful to check the FAQs and the references listed on that page. Also, you can make use of their Molar Calculator tool on Ligation setting (see more from first link).
Good luck with high efficiency!