The invention relates to a multistage fiber amplifier having a first amplifying fiber, at least one further amplifying fiber connected in series with the first amplifying fiber, a pump source, a first pump signal fed to the first amplifying fiber, and a further pump signal fed to the further amplifying fiber. The multistage fiber amplifier is distinguished by the fact that a further pump signal is fed to a further amplifying fiber via a power-dependent attenuation element. The attenuation element is formed in such a way that, as the pump power increases, small further pump signals are attenuated to a greater extent than large further pump signals. The power-dependent attenuation of the further pump signal that is fed to the further amplifying fiber and therefore the increased pump signal that is fed to the first amplifying fiber result in improvements in the noise figure of the multistage amplifier.