We demonstrate an asymmetric dual-loop feedback scheme to suppress external cavity side-modes induced in self-mode-locked quantum-dash lasers with conventional single and dual-loop feedback. In this letter, we achieved optimal suppression of spurious tones by optimizing the length of second delay time. We observed that asymmetric dual-loop feedback, with large (~8x) disparity in cavity lengths, eliminates all external-cavity side-modes and produces flat RF spectra close to the main peak with low timing jitter compared to single-loop feedback. Significant reduction in RF linewidth and reduced timing jitter was also observed as a function of increased second feedback delay time. The experimental results based on this feedback configuration validate predictions of recently published numerical simulations. This interesting asymmetric dual-loop feedback scheme provides simplest, efficient and cost effective stabilization of side-band free optoelectronic oscillators based on mode-locked lasers.