This video overviews the paper, "Balancing Type I error and power in linear mixed effects models" by Matuschek et al (2017). I recently came across a mixed model where the covariance between a random slope and intercept was 1 and wondered why. This paper covered that, but mostly focuses on whether or not simplified random effects structures are okay. Another school of thought is to max it out. Guess what? It can be okay!
All is set up in terms of lmer in R, if that's helpful.