The acceleration of electrons in a parallel electric fields containing randomly distributed, micro double layers is investigated. The study is motivated by recent electric field observations in the auroral acceleration region. Its objective is to determine what effects stochastic versus static parallel electric fields may have on the spectral features of precipitating electrons. The averge electron response as characterized by friction and diffusion coefficients is first analyzed. These coefficients are then used in a Fokker-Planck equation for the altitudinal variation in first analyzed. These coefficients are then used in a Fokker-Planck equation for the altitudinal variation is first analyzed. These coefficients are then used in a Fokker-Planck equation for the altitudinal variation in the electron energy distribution. Electron sources at the top of the acceleration region (plasma sheet electrons) and at its latitudinal edges (ionospheric electrons) are included. It is shown that (1) the plasma sheet source gives rise to ''inverted V'' precipitation, as in quasi-static models, and (2) the edge source is responsible for highly collimated, suprathermal precipitation. The spectral features of the former depend primarily on the average electric field and only weakly on its fluctuations. The properties of collimated precipitation are very sensitive to the microfield, however, owing to trapping phenomena. This analysis represents the first quantitative treatment of collimated electron precipitation; its predictions are in agreement with the observed intensity, pitch angle distribution, energy spectrum, and latitudinal width of edge region precipitation.