Degeneracies of the Orr-Sommerfeld eigenmodes and direct resonances between the Orr-Sommerfeld eigenmodes and vorticity eigenmodes are studied in water-table flow. The sensitivity of the characteristics of these algebraic mechanisms to flow parameters, such as the Reynolds number (R), the slope of the table $(\theta)$, and the material parameter $(\gamma)$, are investigated. It is found that the mechanisms become operative at subtransitional R, and their damping rates decrease with increasing R. When the mean flow profile is slightly distorted from the ultimate parabolic profile, the characteristics of the direct resonances show remarkable variations. Also, some of the algebraic mechanisms in water-table flow are shown to have the same characteristics and modal structures as some of those in plane Poiseuille flow.