Control-flow leakage (CFL) attacks enable an attacker to expose control-flow decisions of a victim program via side-channel observations. Linearization (i.e., elimination) of secret-dependent control flow is the main countermeasure against these attacks, yet it comes at a non-negligible cost. Conversely, balancing secret-dependent branches often incurs a smaller overhead, but is notoriously insecure on high-end processors. Hence, linearization has been widely believed to be the only effective countermeasure against CFL attacks. In this paper, we challenge this belief and investigate an unexplored alternative: how to securely balance secret-dependent branches on higher-end processors? We propose Libra, a generic and principled hardware-software codesign to efficiently address CFL on high-end processors. We perform a systematic classification of hardware primitives leaking control flow from the literature, and provide guidelines to handle them with our design. Importantly, Libra enables secure control-flow balancing without the need to disable performance-critical hardware such as the instruction cache and the prefetcher. We formalize the semantics of Libra and propose a code transformation algorithm for securing programs, which we prove correct and secure. Finally, we implement and evaluate Libra on an out-of-order RISC-V processor, showing performance overhead on par with insecure balanced code, and outperforming state-of-the-art linearized code by 19.3%.