Summary form only given. Two coding algorithms for discrete noiseless channels with input constraints have been analyzed. The first algorithm, which requires infinite-precision arithmetic and is mainly of theoretical interest, can achieve rates as high as channel capacity. The second algorithm is based on the same ideas as the first, but it is much more practical since it uses only finite-precision, floating-point arithmetic. The algorithms are sequential in nature and do not use tables to encode data; as a result, memory requirements are minimal. Experimental results for the finite-precision algorithm have been obtained for the [2, 7] run-length constrained magnetic channel, the charge-constrained channel with a maximum disparity of three, and the telegraphy channel. In the worst of these three cases, encoding at a rate within 0.65% of the capacity was achieved using a precision of only 8 bits. The catastrophic-error-propagation problem was considered, and it was found that, with a slight amendment, the above algorithms can avoid this problem.