In adaptive feedback cancellation, the feedback path must be modeled precisely using as few adaptive parameters as possible to reduce computational complexity and enable rapid convergence. To reduce the number of adaptive parameters, the feedback path is usually modeled with a transfer function composed of an invariant component and a variable component using all-pole, all-zero, and pole-zero filters. These filters may be inefficient, requiring a large number of parameters for their specification, particularly in reverberant environments. In this letter, we present a weighted least-squares algorithm to precisely estimate the common poles of feedback paths, and we then model the invariant basis functions employing a Kautz filter. The Kautz filter is defined by a set of the fixed poles and a corresponding set of tap output weights. The fixed poles are associated with prominent peaks that are common to the measured feedback path frequency responses. The algorithm guarantees unconditionally the stability of the estimated poles of the inferred model. The experimental results using measured acoustic feedback paths from a two-microphone, behind-the-ear hearing aid show that the proposed method provides an accurate model of the feedback paths for a variety of acoustic environments that were not employed in estimating the common poles.