In this letter, we propose a dispersion-aware program-verify algorithm to enable reliable multi-bit operations in HfO2-based RRAM. The significant intrinsic dispersion of the resistive states, typically hindering multi-bit operations, is exploited to devise a program-verify scheme which enables the multi-bit operations with unique properties of failure resilience and adaptability to degradation. We show that an appropriate choice of the algorithm parameters can minimize the average number of cycles needed to program the cell, enabling fast and reliable multi-bit operation. This maximizes the bit/cell ratio and minimizes the dispersion of targeted resistive states.