Curlywurly if you look on the low carb forums there are a lot of people who have cut out sugar or gone no sugar and low carb for things like the blood sugar diet. Personally I think it's easier to cut out starchy carbs at the same time - then once you've done it, only reintroduce then gradually and as wholegrains as the carbs will also kick off cravings like the sugar does.
The first week is absolutely bloody awful. Your insulin levels are high and your body screams at you 'I am starving to death! Eat carbs! Eat sugar! Curl up in a ball and don't move!' You need to drink masses of water as your vagus nerve kicks in and tries to make you faint, having been overstimulated by all the insulin.
However after week 1 your insulin levels return to normal and your body discovers that you aren't starving to death, you can work perfectly normally and you just become a normal amount hungry before each meal, instead of thinking that you are ravenous and NEED FOOD, which is what I was like before giving up.
You also get a lot more energy as now your insulin levels have returned to normal, your body is telling you 'I have enough energy now, just eat enough at each meal, it is OK to do some exercise, I have what I need'.
It's the first week that is the killer - after that it's weird how you can eat much less than before and have double the energy. It's also staggering to discover how much of what you eat is driven by hormones.