When I started learning French, a native speaker told me to exaggerate the sounds. It turns out that I was softening the sounds that are uniquely French because I lacked confidence in my spoken French.

I imagine that the same thing would work for learning to speak English with less of an accent.

That obviously doesn't help you learn the language, but I found that it helped me to speak better (or at least more confidently), so I spoke more. More practice is definitely helpful.