The bit generation algorithm of a quantum random number generator based on photon arrival time differences is improved in terms of the bit generation efficiency and bit generation rate. The method is analyzed mathematically, proving that, in theory, the improved generator still produces random numbers of high quality without the need of resorting to postprocessing algorithms. The effects of nonidealities are quantitatively analyzed to provide bounds for the maximum tolerable deviations from uniformity. Experimental investigations are conducted on a prototype, showing that the method is capable of increasing the rate of bit generation by more than 47% on the same physical architecture.