As you increase your aerobic performance your body will become more efficient at using calories. Aerobic efficiency will also lead to the reduction of the thermogenic effect (heat generated through inefficient use of calories).
Short infrequent HIIT sessions are going to be your best bet to produce caloric deficiencies, while keeping your body inefficient in calorie usage.
Some authors suggest that combination training enhances recovery because of the effeciencies made to the oxidative system (used during rest and low intensity activity), thus helping muscle recovery. In reality, combination training has been shown to reduce gain in muscle girth, maximum strength, and especially speed- and power-related performance.
Aerobic conditioning can be counter-productive to your anaerobic program if you are not careful.