Extracted OIL is my only point. Extracted OILS are very high in calories and very low in nutrients. Extracted OILS tend to be high in the Mediterranean Diet. (So, I think its good the OP said their diet will be low on oil.)
In the end, if weight loss is about maintaining a calorie-deficit (as many health advisers agree, and which I agree), foods that are very high in calories (and devoid of any nutrition) need to be limited.