A new type of electrostatic electron spectrometer is developed, capable of particular sensitive measurements of energy spectra and time-of-flight distributions. This instrument is specifically designed and optimized for laser-pump/x-ray-probe measurements, where photo electrons or Auger electrons from surfaces, clusters, molecular or atomic targets are being measured with high time-resolution at an extremely low detection-noise level. The compact and robust cylinder-symmetrical system is a strongly improved Bessel-box design, featuring electron retardation, a large detection solidangle, about 100% electron transmission (gridless design) and excellent time-resolution. In this paper we describe the principle of operation of this type of spectrometer and various tests. We present quantitative results for electron measurements with different solid-state targets and two different electron-detection systems in comparison to electron-trajectory simulations inside the electrostatic spectrometer fields. Picosecond-pump/probe operation has been tested with high laser power and even the ability to work under femtosecond-pump-probe conditions with electron detection at the BESSY II slicing facility has been proven.