Byzantine agreement protocols in asynchronous networks have received renewed interest because they do not rely on network behavior to achieve termination. Conventional asynchronous Byzantine agreement protocols require every party to broadcast its requests (e.g., transactions), and at the end of the protocol, parties agree on one party's request. If parties agree on one party's requests while exchanging every party's request, the protocol becomes expensive. These protocols are used to design an atomic broadcast (ABC) protocol where parties agree on $\langle n-f \rangle$ parties' requests (assuming $n=3f+1$, where $n$ is the total number of parties, and $f$ is the number of Byzantine parties). Although the parties agree on a subset of requests in the ABC protocol, if the requests do not vary (are duplicated), investing in a costly protocol is not justified. We propose Slim-HBBFT, an atomic broadcast protocol that considers requests from a fraction of $n$ parties and improves communication complexity by a factor of $O(n)$. At the core of our design is a prioritized provable-broadcast (P-PB) protocol that generates proof of broadcast only for selected parties. We use the P-PB protocol to design the Slim-HBBFT atomic broadcast protocol. Additionally, we conduct a comprehensive security analysis to demonstrate that Slim-HBBFT satisfies the properties of the Asynchronous Common Subset protocol, ensuring robust security and reliability.