We recently adapted the conditioned suppression of operant responding method to study fear incubation. We found that food-restricted rats show low fear 2 days after extended (10 d; 100 30-s tone-shock pairings) fear training and high fear after 1–2 months. Here, we studied a potential mechanism of fear incubation: extended food-restriction stress. We also studied whether fear incubation is observed after fear training with a prolonged-duration (6-min) tone conditioned stimulus (CS), and whether conditioned freezing incubates after extended training in rats with or without a concurrent operant task. Conditioned fear was assessed 2 days and 1 month after training. In the conditioned suppression method, fear incubation was reliably observed in rats under moderate food-restriction conditions (18–20 g food/day) that allowed for weight gain, and after extended (10 d), but not limited (1 d), fear training with the 6-min CS. Incubation of conditioned freezing was observed after extended fear training in rats lever-pressing for food and, to a lesser degree, in rats not performing an operant task. Results indicate that prolonged hunger-related stress does not account for fear incubation in the conditioned suppression method, and that fear incubation occurs to a longer-duration (6-min) fear CS. Extended training also leads to robust fear incubation of conditioned freezing in rats performing an operant task and weaker fear incubation in rats not performing an operant task.