The Mg-doping efficiency in GaN layers grown by molecular-beam epitaxy has been studied as a function of the growth temperature, the growth rate, and the Mg beam flux. The Mg cell temperature window for efficient p-type doping is rather narrow, being limited by the GaN n-type background doping density (lower limit) and by the Mg surface coverage that, beyond a threshold, induces a layer polarity inversion (N-polarity), leading to a reduction of the Mg incorporation (upper limit). An increase of the growth temperature avoids this polarity inversion, but the Mg flux must be increased to compensate the strong desorption rate. Thus, a trade-off between both temperatures has to be reached. A reduction of the growth rate has a strong effect on the p-type doping level, yielding up to 7 x 10(17) holes/cm(3) for a total Mg concentration of 1 X 10(19) cm(-3). This high Mg concentration does not seem to generate Mg-related defects or deep traps. (C) 2004 Elsevier B.V. All rights reserved.