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Acoustic reflectometry has been used earlier to estimate the bore profile of a human upper airway and endotracheal tubes using thousands of acoustic pulses. The axial resolution of the profile computed depends on generating a broad frequency response, filtering undesired frequencies and compensating for wave propagation losses. The work presented here shows that acoustic reflectometry may be performed by using few Gaussian-sinusoidal acoustic waves, equally spaced along the bandwidth, and the Ware-Aki algorithm. In this way, the frequency content is controlled, the computational cost is reduced, and the axial resolution is improved. This entails fitting the frequency impulse response, compensating for propagation losses in the amplitude response, and analyzing the phase response. The methodology was validated in the laboratory with an in vitro model of a human upper airway, coupled to an acoustic reflectometer. Only one hundred acoustic waves, with a frequency step of 100 Hz, were needed to reconstruct a profile with an axial resolution within an acceptable margin of error.