The water-waves equations describe the evolution of the free surface of a strip of water, under the influence of gravity. We present here a new result for the existence of solutions, in Sobolev spaces of high-enough but finite regularity. The novelty of this work is an improved dependency on the time interval on which solutions can be defined, in the presence of a (non-flat) bathymetry. This is a joint work with Benjamin Melinand (Université de Strasbourg)