A sequence of optically stimulated luminescence measurements was made on each of 8,961 grains from three sand samples from Blombos on the southern Cape coast. One sand unit overlay Middle Stone Age deposits in Blombos Cave. The measurement sequence, the single aliquot regenerative dose protocol, was used to obtain values for the total effective radiation dose to which each grain had been exposed since burial. A series of checks was carried out on each grain to ensure that the luminescence signals were reproducible, and that they were derived from quartz. This led to acceptance of less than 5% of the grains. An estimate of the radiation dose for the sand unit was obtained by combining the values using the central age model. In order to use a larger number of grains that might be representative of the sand unit, the radiation dose was also estimated by using the signal from the above grains, combined with the signals from those grains that had lower signals, but nonetheless contributed to the total light sum; this utilised between 9 and 18% of the grains. This enables us to obtain estimates of the ages as 67.3+/-3.8 ka, 65.6+/-2.8 ka and 68.8+/-3.0 ka for the three samples. These values agree with ages obtained using the single aliquot regenerative dose protocol for aliquots composed of several hundred grains.