The inverse-filtering of acoustic impulse responses (AIRs) can be achieved with existing methods provided a good estimate of the channel is available and the observed signals contain little or no noise. Such assumptions are not generally valid in practical scenarios, leading to much interest in the issue of robustness. In particular, channel shortening (CS) techniques have been shown to be more robust to channel estimation error than existing approaches. In this paper we investigate CS using the relaxed multichannel least-squares (RMCLS) algorithm in the presence of both channel error and additive noise. It is shown quantitatively that shortening the acoustic channel to a few ms duration is more robust than attempting to equalize the channel fully, giving better resultant sound quality for dereverberation. A key point of this paper is to provide an explanation for this added robustness in terms of the equalization filter gain. We provide simulation results and results for practical settings using speech recordings and room impulse response measurements from a real acoustic environment.