The emerging Zoned Namespace (ZNS) interface helps flash-based SSDs achieve high performance by dividing the logical space into fixed-size zones. Typically, a zone is mapped to blocks across multiple dies to achieve I/O parallelism. Small zones can make better use of space and are therefore widely studied. However, a small zone fails to be mapped to blocks residing on all dies, causing underutilized die-level parallelism. Meanwhile, a fine-grained (i.e., plane-level) parallelism is rarely exploited for ZNS SSDs due to a strict limitation mandating that only the same type of operation can be simultaneously performed on the same address across different planes within a die. To address these issues, this paper proposes a novel small-zone ZNS-SSD design with dynamic zone mapping, named Para-ZNS. First, a new parallel block grouping module is devised to group blocks across all planes from multiple dies as a basic unit to be mapped to a zone. Such a basic mapping unit achieves parallelism among multiple dies and plane-level parallelism. Then, a die-parallelism identification module is implemented to locate idle dies. Subsequently, to fully exploit the die-level parallelism, a dynamic zone mapping scheme is employed to intelligently map the basic mapping units on the identified idle dies to open zones. The evaluation results based on a widely-used I/O tester (FIO) demonstrate that Para-ZNS improves the bandwidth by 3.42× on average in comparison to state-of-the-art work.