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Recently, non-Lambertian models for perspective shape from shading (PSFS) have received attention in the literature. The Phong-based PSFS model combining Lambertian and specular reflection has been shown to give good results for objects in real-world images. In this paper, we present at hand of this model the first analysis of a non-Lambertian PSFS model in the literature. We show mathematically and experimentally how crucial the specular part of the model is for the reconstruction. Moreover, we give a detailed analysis of the Hamiltonian defining the model. While the non-Lambertian reflectance is generally assumed to lead to numerical difficulties, this investigation shows that an efficient fast marching scheme can be applied successfully without losing depth information. Our work represents a first step towards the thorough understanding of non-Lambertian PSFS models.