In these notes we generalize the following result due to R. Accola: Given a hyperelliptic Riemann surfaceSof genusg⩽2 andna non-negative integer, there is a smoothn-sheeted covering, whereRis a hyperelliptic Riemann surface. We show that the above result extends to the family of η-hyperelliptic Riemann surfaces as: Given a η-hyperelliptic Riemann surfaceSof genusg⩽2, a η-hyperelliptic involution τ:S→Sand a non-negative integern, there is a smoothn-sheeted covering, whereRis ahyperelliptic Riemann surface for which τ lifts as a-hyperelliptic involution, and