One of the bottlenecks preventing Deep Reinforcement Learning algorithms (DRL) from real-world applications is how to explore the environment and collect informative transitions efficiently. The present paper describes bounded exploration, a novel exploration method that integrates both 'soft' and intrinsic motivation exploration. Bounded exploration notably improved the Soft Actor-Critic algorithm's performance and its model-based extension's converging speed. It achieved the highest score in 6 out of 8 experiments. Bounded exploration presents an alternative method to introduce intrinsic motivations to exploration when the original reward function has strict meanings.