How to remove grey borders around individual entries in ggplot2 legend when using theme_bw?

Question

I have the following code in R:

library(ggplot2)
theme_set(theme_bw())
p <- ggplot(mtcars, aes(wt, mpg))
p <- p + geom_point(aes(colour = factor(cyl)))
p

Resulting in this:

Each legend entry has a grey border around it. How to remove it?

Answer 1

Just add

+ theme(legend.key = element_rect(colour = NA))