Lots of us have discovered that it isn't just the sugars but all the carbs. I have seriously cut out as much of the starchy carbs as I can so have not been eating bread, potatoes, rice, pasta etc. Porridge has been my biggest sacrifice but I have managed to get my levels right down.
I eat fish, meat, cheeese and eggs with salad stuff, veggies ( holding back on the roots) and certain fruits with nuts and seeds and I use a carb counter book to help with the food choices. It works! It would be worth you trying this and testing to see how your food affects your own levels.