Human sound localization in the mid-saggital plane (elevation) relies on an analysis of the idiosyncratic spectral shape cues provided by the head and pinnae. However, because the actual free-field stimulus spectrum is a-priori unknown to the auditory system, the problem of extracting the elevation angle from the sensory spectrum is ill-posed. Here we test different spectral localization models by eliciting head movements toward broad-band noise stimuli with randomly shaped, rippled amplitude spectra emanating from a speaker at a fixed location, while varying the ripple bandwidth between 1.5 and 5.0 cycles/octave. Six listeners participated in the experiments. From the distributions of localization responses toward the individual stimuli, we estimated the listeners' spectral-shape cues underlying their elevation percepts, by applying maximum-likelihood estimation. The reconstructed spectral cues resulted to be invariant to the considerable variation in ripple bandwidth, and for each listener they had a remarkable resemblance to the idiosyncratic head-related transfer functions (HRTFs). These results are not in line with models that rely on the detection of a single peak or notch in the amplitude spectrum, nor with a local analysis of first- and second-order spectral derivatives. Instead, our data support a model in which the auditory system performs a cross-correlation between the sensory input at the eardrum-auditory nerve, and stored representations of HRTF spectral shapes, to extract the perceived elevation angle.