We investigate the bifurcation of small-amplitude limit cycles in generalized Liénard equations. We use the simplicity of the Liénard family, to illustrate the advantages of the approach based on Bautin ideals. Essentially, this Bautin ideal is generated by the so-called Lyapunov quantities, that are computed for generalized Liénard equations and used to detect the presence of a Hopf-Takens bifurcation. Furthermore, the cyclicity is computed exactly.