I have some experience with what you're talking about.
I lost a little less than 20lbs of fat, while building a little bit of muscle. I do competitive Olympic lifting so it was incredibly important to me to maintain or gain my muscle mass over the course of weight loss.
I have done so through an extremely low-carb diet (<50g on rest days, 50g-100g on workout days), somewhat restricting calories (aiming for 1800-2100kcal/day for an 187lbs female, now 171lbs), and being fanatic about my protein intake--I started out getting 1g/lbs and now aim for 1.4-1.5g/lbs. I actually went through a six-week squat cycle and did excellently. I failed to produce a good max squat at the end, but that was due to a new 70-90 hour/week completely derailing my lifting, sleeping, and eating for the last week or so of it rather than the diet.
My lifts are improving and as far as I can tell I haven't lost any muscle mass. I eat sweet potatoes for post-workout carbs, and otherwise the most high-glycemic thing I eat is maybe berries in cottage cheese in the morning. Otherwise it's all green vegetables.
I could probably be getting stronger faster if I was eating a higher number of calories, but for my weight-loss goals I've been extremely pleased with how it's been working out.