Homotopic grayscale thinning leads to over-connected skeleton when applied on noisy images. To avoid this phenomenon, the parametric thinning relaxes the initial constraint by lowering low contrast crests, peaks and ends, according to a parameter related to the noise and contrast of the image and under the constraint of ascendant gray level processing. Even if the statistical control of this parameter leads to a local adjustment and to a standardization of the thinning parameter, this method still produces spurious branches. In fact, the lowering criterion for peak and end notions becomes unadapted while the image dynamic changes during the thinning process. To avoid this phenomenon, we propose to revise and unify these lowering criteria. Consequently, we update the statistical test design by taking into account the gray level of the treated pixels to better fit to lowerable pixels definition. Results of our contribution are compared to the initial parametric thinning.