Syscall interposition is crucial for tools that monitor/modify application behavior. Mainstream OSes have, therefore, provided syscall interposition APIs for years, but these often incur prohibitive performance penalties in syscall-intensive applications. Recent work showed how to reduce this overhead by rewriting syscall instructions¹¹Throughout this paper, we will use the term 'syscall instruction' to refer to both the x86 SYSCALL and SYSENTER instructions. to invoke the interposer directly, avoiding expensive mode/context switches. However, these methods may not locate/rewrite all relevant instructions, which is essential for many applications. Our key insight is to combine the aforementioned techniques to efficiently intercept all system calls. We present lazypoline, a tool that uses slow kernel interfaces to exhaustively locate valid syscall instructions upon their first use, and then lazily rewrites them to invoke the interposer directly in all subsequent executions. We extensively evaluate lazypoline on micro- and macrobenchmarks and show that it is non-intrusive, fully exhaustive, and it achieves the efficiency of pure rewriting, even for datacenter-scale syscall-intensive workloads.