Reduce carbs period if you want to lower A1c. Side effect is you lose weight too.
Just reducing sugar is not enough, though. Decreasing carbs, while increasing fats, causes the body to revert to fat stores for energy. Weight loss is faster and greater on the high fat, moderate protein, very low carb diet. Doesn’t sound like eating a lot of fat would work, but it does. The studies done have shown so, plus, bad cholesterol levels drop, heart disease drops, despite high fat (including animal fat) intake. I lost around 8 lbs (one dress size) in a couple of weeks on this diet, and my A1c, which is never too high, but moderately so, was the lowest ever. It was just a tad higher than a non-diabetic. And being allowed extra fat, kind of makes up for the deprivation you feel when you take out most of the carbs in your diet. Eating a cupful of strawberries with a huge blob of whipped heavy cream and a little natural sugar substitute, doesn’t feel like dieting, but it is.