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My experience is that it takes some time to adjust, but given proper amounts of rest the body learns to adapt for endurance work. Not a problem at all for me.

I have also done powerlifting in the past whilst on Atkins, and suffered no major ill effects. I just increased carb intake and made sure not to exhaust energy stores before hand.

Lifting is a little more difficult because "fast burst" energy is required, but there are athletes that can get away with lifting heavy whilst on low carb diets.

I didn't do too badly myself.