Maximal Fat Loss with Minimal Strength Loss

After too much time spent on dirty bulking and a more powerlifting based training protocol, I have decided its time to take a leaf from the bodybuilders book and “cut” down so to speak. Many discuss cuttings effect on an individuals lean muscle mass but I am more concerned about something thats far less frequently talked about, maintaining current strength levels.

My program is very basic. The more simplified my training is the easier it is to follow and succeed in my personal experience. I squat, Dead, Dip, Pull&Chin, military press and Bench. In the past I have noted some interesting information.

As i hve cut down, my squat dip and pull up remain similar but all free weight pressing movemnts drop fairly drastically. Perhaps its due to the fact these movements involve lifting your bodyweght so it is be easier if i weigh less? Thoughts on using the above basic compound exercises to achieve my goal of a lower body fat% and a maintainance of strength levels. Complexes, supersets, EDT, decrease rest higher volume? Thoughts?