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When you cut out legumes, grains and their derivative products and instead focus on nutrient-dense whole foods, such as wild seafood, meat, non-starchy vegetables and some fruit, you end up by default eating a lower amount of carbohydrate when compared to a grain-centric Standard American Diet. However, Paleo doesn’t have to be low-carb. If you're highly active, most credible proponents of the Paleo diet would suggest you consume carbohydrates commensurate to your activity levels.
One larger randomized controlled trial followed 70 post-menopausal Swedish women with obesity for two years, who were placed on either a Paleo diet or a Nordic Nutrition Recommendations (NNR) diet.  The Paleo diet provided 30% of total calories from protein, 40% fat (from mostly monounsaturated and polyunsaturated fats) and 30% carbohydrates. It included lean meats, fish, eggs, vegetables, fruits, berries, nuts, avocado, and olive oil. The NNR diet provided less protein and fat but more carbohydrate with 15% protein, 25-30% fat, and 55-60% carbohydrates, including foods similar to the Paleo diet but also low-fat dairy products and high-fiber grains. Both groups significantly decreased fat mass and weight circumference at 6 and 24 months, with the Paleo diet producing greater fat loss at 6 months but not at 24 months. Triglyceride levels decreased more significantly with the Paleo diet at 6 and 24 months than the NNR diet.