Perturbation theory and boss models for rough surface scattering are compared for the case of a surface bossed with oblate hemispheroids (heighta≤radiusb). In particular, the surface consists of identical, hard, hemispheroidal bosses sparsely and independently distributed on a hard plane by means of a uniform probability law. To apply perturbation theory we compute the surface correlation function, operate on that function, and compute an effective boundary admittance. Finally, we compare that admittance with (farfield) near‐exact results for hemispherical bosses and for oblate hemispheroidal bosses. Calculations of the magnitude of the reflection coefficient ‖R‖ are presented showing that for low frequencies, i.e.,kb=0.1, the discrepancy is approximately 70% fora=bbut less than 10% fora/b=0.1. In general, the error decreases as grazing angle increases and decreases asa→0. Thus, at low frequencies perturbation theory is shown to give excellent results for ‖R‖ whena/b≪1, despite the discontinuous and infinite slope in the surface where the bosses meet the base plane. We also examine the effects of increasing frequency for hemispherically bossed surfaces, and in particular, we see errors as large as 3 dB for sparse, hemispherical bosses witha=b=5 m and frequencies less than 60 Hz. We conclude that perturbation theory is excellent in the case of oblate hemispheroids, shows significant percentage errors for hemispheres and should not be used for prolate hemispheroids.