Lipman Bers showed that one can cut a finite area hyperbolic surface along disjoint "short" curves so that the result is a set of three holed spheres. Here the term "short" means that the length of each curve is bounded by a constant (Bers' constant $B$) which only depends on the topology of the surface and not on the metric. The best bounds (upper and lower) on Bers' constant are due to Peter Buser who also conjectured the existence of universal constant $C$ such that Bers' constant is bounded above by $C$ times the square root of the area (which is linear in the Euler characteristic). The goal of the talk will be to present a solution to the conjecture for punctured spheres and hyperelliptic surfaces. This is joint work with Florent Balacheff.