HAETAE is a new lattice-based signature scheme that improves upon Dilithium by reducing signature and verification key sizes by up to 39% and 25%, respectively. It is based on the Fiat-Shamir with Aborts paradigm and is designed for space-limited applications. HAETAE uses bimodal rejection sampling and hyperball uniform distributions, which allows for smaller signatures and efficient protection against implementation attacks. The scheme is implemented with a portable, constant-time reference implementation, an optimized AVX2 version, and a Cortex-M4 implementation. HAETAE is also resistant to side-channel attacks and is suitable for use in IoT and embedded systems. The scheme is secure under the assumption of the hardness of module versions of the lattice problems LWE and SIS in the Quantum Random Oracle Model. HAETAE's design includes a novel key generation algorithm and efficient rejection sampling, which contribute to its compactness and security. The scheme is compared with Dilithium and Falcon in terms of security levels, signature sizes, and performance. HAETAE's signature compression and fixed-point arithmetic enable efficient signing and verification, making it suitable for resource-constrained environments. The scheme is implemented with a focus on constant-time execution and resistance to side-channel attacks, ensuring its suitability for practical deployment.HAETAE is a new lattice-based signature scheme that improves upon Dilithium by reducing signature and verification key sizes by up to 39% and 25%, respectively. It is based on the Fiat-Shamir with Aborts paradigm and is designed for space-limited applications. HAETAE uses bimodal rejection sampling and hyperball uniform distributions, which allows for smaller signatures and efficient protection against implementation attacks. The scheme is implemented with a portable, constant-time reference implementation, an optimized AVX2 version, and a Cortex-M4 implementation. HAETAE is also resistant to side-channel attacks and is suitable for use in IoT and embedded systems. The scheme is secure under the assumption of the hardness of module versions of the lattice problems LWE and SIS in the Quantum Random Oracle Model. HAETAE's design includes a novel key generation algorithm and efficient rejection sampling, which contribute to its compactness and security. The scheme is compared with Dilithium and Falcon in terms of security levels, signature sizes, and performance. HAETAE's signature compression and fixed-point arithmetic enable efficient signing and verification, making it suitable for resource-constrained environments. The scheme is implemented with a focus on constant-time execution and resistance to side-channel attacks, ensuring its suitability for practical deployment.