This response by one of the dietitians (Dietitians Weigh in on the Low Carb/Ketogenic Diet) is something I’ve not heard of before (at least by this name). The suggestion is that this alternate diet is better for diabetics. Here’s the comment:
I would consider suggesting the Consistent Carbohydrate Diet.
Here’s the Consistent Carbohydrate Diet (Int J Pediatr Endocrinol. 2009; 2009: 469623. The Origin of the Constant Carbohydrate Diet. Charles Herbert Read, Jr.). I believe this is what the dietitian I visited in the 1990’s was teaching (or something similar). This diet was developed in 1951.
The developer of the diet had “children with insulin-dependent diabetes” as patients and their mothers had trouble figuring out the standard ADA diet for diabetics. It was just too complicated back in 1951. From the history above:
This prestigious ADA exchange diet was taught in virtually all the diabetic centers in Canada and the United States. Its concept was that any food which contains an equivalent amount (within 3 grams) of carbohydrate, fat, and protein could be substituted for a similar food if they were in the same food group. The groups were Milk, Meat (sometimes divided into high- or low-fat subgroups), Vegetables, Breads, and Fats. For example, if an eight-ounce glass of skim milk was substituted for an eight-ounce glass of whole milk containing 10 grams of fat, where would one find the 2 fat exchanges that were needed.
The implication was that the insulin need was related to the total calories ingested.
The last line is a solid objection. No need to inject for fat.
It made little sense to me that while insulin is necessary to produce fat, it has a negligible role in its catabolism. So why to pay attention to fat in so far as the insulin requirement is concerned?
The author also observed that people tend to eat a consistent amount of protein so that could be held constant day to day. Remember that Type 1 diabetics typically injected for half the grams of protein (as compared to carbohydrates).
This was an astute observation in that in the end it meant that people who inject insulin only need to track carbohydrates. They will be giving variable amounts of Insulin based on carbs and a constant amount (basal amount) based on the protein levels. So this insight was to keep carbs constant day to day.
I concluded that because insulin is required for the metabolism of the dietary carbohydrate, an appropriate diet for diabetes is one in which the carbohydrate content of each of the meals, although different in amounts at breakfast, lunch, and dinner, would be the same from day to day. Variations in the protein and fat content are ignored.
The method in a nutshell is:
Only the carbohydrate is counted, so any food may be included in the diet by referencing a Carbohydrate Guide and staying within 3 grams of the decided amount of carbohydrates at each eating time. This is the Constant Carbohydrate diet.
This all led to increased compliance in Type 1 diabetics.
After she had used this diet for several months, Adams  noted that although at first the mothers were confused by this seemingly drastic change, they and the patients easily and even happily adapted to this new way of thinking and doing, especially those of different ethnic origins. Her reaction was typical of the responses of each dietitian who subsequently began using the diet.
From that I would conclude that there’s nothing inherently contradictory between a Low Carb diet and a Constant Carbohydrate diet. The Low Carb diet is just less than 20 or 30 grams of carbs a day.
The insights of the author are probably part of my own thought process. Controlling carbs is good. Keeping carbs at low levels is good. Most problems come from large amounts of carbs.