Exploration for low-outgassing materials for use in ultrahigh vacuum and extreme high-vacuum systems is one of the most important topics of a vacuum researcher. We have found that a copper alloy containing 0.2% beryllium (0.2% BeCu) can attain an extremely low hydrogen outgassing rate of 10(-14) Pa (H-2) m/s order. Almost the entire surface of 0.2% BeCu is dominated by a BeO layer, after a 400 degreesC x 72 h prebakeout treatment in an ultrahigh vacuum. This layer functions as a barrier to the processes of oxidization and permeation of hydrogen. In addition, this layer resists carbon contamination. Temperature-programmed desorption spectra show only a single peak for water at 150 degreesC and small quantities of any other desorption gases. Therefore, an in situ bakeout process in which the temperature simply ramps up to 150 degreesC and immediately ramps back down is enough for degassing; it does not. require an ordinary sustained-temperature bakeout. Using an outgassing sample consisting of 0.2% BeCu disks housed in a 0.2% BeCu nipple chamber, a lowest outgassing rate of the 5.6 x 10(-14) Pa (H-2) m/s was measured by the pressure-rise method after pump cutoff. The pressure-rise versus time curve was completely nonlinear. It rises over time to a constant slope of 1/2 in a log-log plot, due to hydrogen diffusion from the bulk, but this requires over a week at room temperature. The hydrogen outgassing from the 0.2% BeCu bulk is completely dominated by a diffusion-limited mechanism. This article will describe why we obtain such low-outgassing rates with 0.2% BeCu. It is based on the observed surface changes with prebakeout treatment seen by x-ray photoelectron spectroscopy, and the improvement of hydrogen outgassing measurements by the pressure-rise method. A comparison is made to ordinary stainless steel. In addition, the concept of an outgassing reduction method will be discussed from a review of the published ultralow-out-assine, data and reduction methods. (C) 2004 American Vacuum Society.