This paper proposes an efficient time-varying step-size adaptation algorithm implemented within an in-service non- intrusive measurement device (INMD) in public switched telephone networks (PSTNs). The adaptation step-size is obtained from the correlation of the input speech signal. The effect of the correlation method is described and the variable step-size is derived. The in-service non-intrusive measurement system of interest is used to monitor the delivered Quality of Service (QoS) by monitoring the echoes in the telephony network. INMDs are usually based on a class of least mean square (LMS) digital adaptive filters (DAFs). The performance criterion is defined by the modelling convergence rate derived from the optimal Wiener weights, and the excitation for the DAFs is conversational speech. Experimental observations have shown that divergence occurs during the low energy unvoiced segments in high-noise environments. The optimum adaptation step-size minimises such divergence by using low step-sizes d uring unvoiced periods. This result is then compared with a perfect divergence detector (PDD), which employs the unknown Wiener weights, a technique applicable in simulations only. The optimal step-size method reported produces a significant improvement in the system's performance in a noise-impaired environment where the near-end speech and echo path speech are contaminated with noise. Original simulation results show a modelling misadjustment improvement of 30.3 dB and 11.9 dB for noise free and noisy (signal to noise ratio, s/N of 5 dB) near- end speech respectively, all at a far-end echo to noise ratio (e/N) of 0 dB over 1 second adaptation.