1. A method of storing a first plurality of input bits in a plurality of memory cells, comprising: (a) providing a first mapping of bit patterns to cell states of the memory cells; (b) mapping the first plurality of input bits to a first plurality of transformed bits that is larger in number than the first plurality of input bits, using a first shaping encoding that has a downward asymptotic bias with respect to the first mapping of bit patterns to cell states; (c) programming at least a portion of the first sub-plurality of the memory cells to store the first plurality of transformed bits according to the first mapping of bit patterns to cell states; and (d) erasing the at least portion of the first sub-plurality of the memory cells before programming the at least portion of the first sub-plurality of the memory cells to store any other bits.