Software vulnerabilities undermine the security of applications. By blocking unused functionality, the impact of potential exploits can be reduced. While seccomp provides a solution for filtering syscalls, it requires manual implementation of filter rules for each individual application. Recent work has investigated approaches to automate this task. However, as we show, these approaches make assumptions that are not necessary or require overly time-consuming analysis. In this paper, we propose Chestnut, an automated approach for generating strict syscall filters with lower requirements and limitations. Chestnut comprises two phases, with the first phase consisting of two static components, i.e., a compiler and a binary analyzer, that statically extract the used syscalls. The compiler-based approach of Chestnut is up to factor 73 faster than previous approaches with the same accuracy. On the binary level, our approach extends over previous ones by also applying to non-PIC binaries. An optional second phase of Chestnut is dynamic refinement to restrict the set of allowed syscalls further. We demonstrate that Chestnut on average blocks 302 syscalls (86.5 %) via the compiler and 288 (82.5 %) using the binary analysis on a set of 18 applications. Chestnut blocks the dangerous exec syscall in 50 % and 77.7 % of the tested applications using the compiler- and binary-based approach, respectively. For the tested applications, Chestnut blocks exploitation of more than 61 % of the 175 CVEs that target the kernel via syscalls.