Whatever 'first have to deal with' is up to the individual, with (or without) input from his or her doctor.
The A to Z study seems to point out that the Zone Diet is the best for micronutrients:
(from the study)
'Energy intake decreased from baseline in all 4 groups but was similar between groups. At 8 wk, a significant proportion of individuals shifted to intakes associated with risk of inadequacy (P < 0.05) in the Atkins group for thiamine, folic acid, vitamin C, iron, and magnesium; in the LEARN group for vitamin E, thiamine, and magnesium; and in the Ornish group for vitamins E and B-12 and zinc. In contrast, for the Zone group, the risk of inadequacy significantly decreased for vitamins A, E, K, and C (P < 0.05), and no significant increases in risk of inadequacy were observed for other micronutrients.'
The Zone diet is one of the more difficult diets to follow, if you are going to adhere to exactly the right proportions of carbs, protein, and fats. It's more difficult for people who, for example, have trouble with measuring food for the WW diet. This is one drawback to that diet. But if you're concerned with micronutrients, it's a good diet!
Micronutrient deficiencies don't occur in MOST weight loss diets (your words, not the study's) - the study only focused on four diets. There are many diets.
The conclusion states:
'Weight-loss diets that focus on macronutrient composition should attend to the overall quality of the diet, including the adequacy of micronutrient intakes. Concerning calorie-restricted diets, there may be a micronutrient advantage to diets providing moderately low carbohydrate amounts and that contain nutrient-dense foods.'
http://www.ncbi.nlm.nih.gov/pubmed/20537171
The conclusion of THAT study was:
'These findings are significant and indicate that an individual following a popular diet plan as suggested, with food alone, has a high likelihood of becoming micronutrient deficient; a state shown to be scientifically linked to an increased risk for many dangerous and debilitating health conditions and diseases.'
It did not use human participants to judge the micronutrient quality of the diets studies (Atkins for Life, DASH, Best Life Diet, South Beach) but went by the menus, directions and restrictions stated in the books. If you followed the books menus to the letter, in other words (who does that?).
That study mentioned that there are correlations between nutrient deficiency and obesity. But correlation is not causation. Despite that, there is a sentence in the study that uses the word 'cause' regarding a study of overweight mothers who are nutrient-deficient in Egypt and clearly, there was no causality shown there. AND the study was authored by a person who is in the process of developing a multivatamin for his own supplement company.
An interesting study, nonetheless, requiring nothing but strict adherence to the diets to provide the measured nutrients.
(Yet, we don't know everything about micronutrients; we don't even know if there are micronutrients not yet identified, which make eating something different than taking a supplement with the same particular vitamin content.)
'the change from a carb rich diet to a low carb diet allows the weight to drop off without the need for much effort at all, and when you are successfully losing more than 2lbs a week each week every week, these positive rewards keep you on track without any or much effort.'
That is the ideal experience with low-carbing. The forum's collective experience, as evidenced by reports in journals, tell a different story. Dieting is dieting.
With Atkins, and any very low-carb diet, you lose 'water weight' the first week or two, and then your body adjusts. Still, that 'whoosh' (as it's called here) is nice. But sticking to the diet (adherence) is a matter of the individual, and it is not easy for everyone. And it really is not easy ALL the time for everyone.
The two pounds a week you mention is what WW uses as a normal weekly weight loss if you stick to THEIR diet, which essentially ends up being fewer calories than you ate before the diet.
A diet is a diet is a diet. It's up the individual to choose, because it's up to the individual to adhere.