An inlet sieve for a self-priming floating pump features a bottom wall that is carried in a position that underlies the inlet of the self-priming floating pump at a distance therebelow with the inlet of the pump aligned with an axis that passes through the bottom wall of the sieve. A perforated outer wall of the sieve stands upward from a top side of the bottom wall and extends about the axis. The bottom wall features an outer area that spans inwardly from the perforated outer wall toward the axis, and a protuberance that bulges upwardly from the outer area to an apex of the protuberance that is situated at the axis. Water flowing inwardly toward the protuberance from different radial directions is directed smoothly upward into the inlet of the pump with minimal turbulence in order to optimize the performance of the pump.