Software robustness is an ever-challenging problem in the face of today's evolving software and hardware that has undergone recent shifts. Instruction-grain monitoring is a powerful approach for improved software robustness that affords comprehensive runtime coverage for a wide spectrum of bugs and security exploits. Unfortunately, existing instruction-grain monitoring frameworks, such as dynamic binary instrumentation, are either prohibitively expensive (slowing down applications by an order of magnitude or more) or offer limited coverage. This work introduces BugSifter, a new design that drastically decreases monitoring overhead without sacrificing flexibility or bug coverage. The main overhead of instruction-grain monitoring lies in execution of software event handlers to monitor nearly every application instruction to check for bugs. BugSifter identifies common monitoring activities that result in redundant monitoring actions, and filters them using general, light-weight hardware, eliminating the majority of costly software event handlers. Our proposed design filters 80-98% of events while monitoring for a variety of commonly-occurring bugs, delegating the rest to flexible software handlers. BugSifter significantly reduces the overhead of instruction-grain monitoring to an average of 40% over unmonitored application time. BugSifter makes instruction-grain monitoring practical, enabling efficient and timely detection of a wide range of bugs, thus making software more robust.