THIS is to report an obvious (once one has thought of it) improvement in speed of histogram sampling for simulations that we have recently introduced, which has approximately doubled sampling speed and in one instance reduced run times from 11 to 8 min, although some loss of accuracy is entailed. When sampling on a computer from a standard distribution the cumulative probability density function is considered.' With histograms, sampling is normally performed by multiplying the total cumulative count by a positive random fraction and seeing in which cell of the histogram this cumulative count occurs. This procedure involves searching the histogram array, whereas our new method of sampling using the inverse cumulative histogram requires only two accesses of the histogram array and thus is much quicker. The histogram is initially converted to a cumulative distribution function Y = F(X) assuming a uniform distribution within the cells of the original histogram. The values of X for a uniform series of values of Y are stored in an array, called the inverse cumulative array. For illustration in this note assume that the array has 100 elements, the first element gives the cell value of the first percentile point of the distribution and so forth. A random fraction is obtained, multiplied by 100 and the integer part M gives the appropriate index in the inverse cumulative array. The fractional part of the random number N then gives the position in this inverse cumulative cell assuming a uniform distribution within the cell, so the sample value returned is Xm + (Xm+, Xm)*N which approximates to the original histogram. More elaborate interpolation both for the initial transformation and subsequent sampling is obviously possible. The transformation to the array Xi is non-reversible, except for special cases, such as where the original histogram is a uniform distribution, since information about the original histogram is lost in the transformation. The histogram built up by sampling in this manner from the inverted cumulative array consists of 100 rectangular blocks of varying height and width, but uniform area. Thus tails on the original histogram are reproduced as long low rectangles, introducing an undesirable bias and for this reason this method is best avoided if the original histogram has a long low tail. It is sensible to arrange that no samples are returned for cells outside the main body of the original histogram. Cells that were empty within the main body of the original