Recent controlled-channel attacks exploit timing differences in the rudimentary fetch-decode-execute logic of processors. These new attacks also pose a threat to software on embedded systems. Even when Trusted Execution Environments (TEEs) are used, interrupt latency attacks allow untrusted code to extract application secrets from a vulnerable enclave by scheduling interruption of the enclave. Constant-time programming is effective against these attacks but, as we explain in this paper, can come with some disadvantages regarding performance. To deal with this new threat, we propose a novel algorithm that hardens programs during compilation by aligning the execution time of corresponding instructions in secret-dependent branches. Our results show that, on a class of embedded systems with deterministic execution times, this approach eliminates interrupt latency side-channel leaks and mitigates limitations of constant-time programming. We have implemented our approach in the LLVM compiler infrastructure for the Sancus TEE, which extends the openMSP430 microcontroller, and we discuss applicability to other architectures. We make our implementation and benchmarks available for further research.