The problem of coding low-entropy information sources is considered. Since the run-length code was offered about 50 years ago by Shannon, it is known that for such sources there exist coding methods much simpler than for sources of a general type. However, known coding methods of low-entropy sources do not reach the given redundancy. In this correspondence, a new method of coding low-entropy sources is offered. It permits a given redundancy r with almost the same encoder and decoder memory size as that obtained by Ryabko (see ibid., vol.40, p.96-9, 1994) for general methods, while encoding and decoding much faster.