Wheelset bearing compound faults are observed as impulses in the vibration measurements but immersed in noise. The morphological undecimated wavelet (MUW) is an effective tool for recovering fault-related impulses from vibration mixtures. To date, the reported MUWs adopt an identical morphological operator in each level of decomposition without exception. However, effectively capturing signal signatures by repeatedly using a noise elimination operator, an impulse extraction operator, or even the product of two operators is unattainable. Spurred by this deficiency, in this paper, we propose a multi-operator MUW (MOMUW). A three-level structure: noise reduction, impulse extraction, and further denoising and feature enhancement, is developed in the MOMUW, and different morphological operators are designed for each decomposition level to more purposefully denoise and extract impulse features. The developed MOMUW is applied to measured wheelset bearing vibration data, with the results demonstrating that it can accurately detect wheelset bearing compound faults. Compared with the reported MUWs, the proposed approach presents superior performance. Furthermore, MUWs with varying operators and levels are analyzed and compared. Their success and failure in bearing fault diagnosis are interpreted and discussed, laying a theoretical foundation for constructing new MUWs.