Estimating room impulse responses (RIRs) has a number of applications, including personalized audio, analyzing and improving acoustic behavior of concert halls, listening room compensation, sound source localization, and many others. RIRs have been estimated in essentially the same fashion for the last 50 years: Compute the cross correlation between a signal played at point A, and the signal received at point B. Best results are obtained when the signal played is white noise, or a maximum length sequence. No prior knowledge is exploited in computing the RIR, which is simply assumed to be the cross correlation between played and received signals. In contrast, research in adaptive RIR estimation (a.k.a. adaptive Acoustic Echo Cancellation) has made huge progress by (among other things) incorporating models for the RIR. In this paper we propose a new RIR estimation technique, based on a maximum a posteriori formulation. More specifically, we estimate the room reverberation time, as well as the room noise level, and use those as priors for the RIR estimation. Comparison with ground truth shows an average improvement of 12 dB compared to traditional methods.