A motor-and-pump unit having an electric motor in combination with a housing of the pump. The pump has at least one displaceable pump piston. To that end, on the side toward the pump housing and originating at one end wall, the electric motor has a bearing neck, which is tubular and into which the pump housing protrudes. This bearing neck fixes an outer ball bearing race of a ball bearing for a shaft of the electric motor. Protruding from the ball bearing is a shaft end that carries an eccentric element for moving the at least one pump piston. The eccentric element is disposed at an axial spacing from an inner ball bearing race that surrounds the shaft in stationary fashion. The eccentric element is brought directly up to the inner ball bearing race, and the inner ball bearing race and the eccentric element are embodied as a one-piece, multifunctional component. This one-piece construction offers the advantage that both the inner ball bearing race and the eccentric element firmly surround the end of the shaft like a reinforcing sleeve and thus reinforce this shaft end. Furthermore, bringing the eccentric element close to the ball bearing reduces the bending moment that tends to cause warping.