1. A method of attempting to store, successively, in a plurality of memory cells, a first plurality of input bits and a second plurality of input bits, comprising: (a) providing a mapping of bit sequences to cell levels of the memory cells; (b) transforming the first plurality of input bits to a first plurality of transformed bits, using a first transformation; (c) programming at least a first portion of the memory cells to store the first plurality of transformed bits according to the mapping; and (d) subsequent to the programming of the at least first portion of the memory cells, and without erasing at least a second portion of the memory cells that includes the at least first portion of the memory cells: (i) determining, for the at least second portion of the memory cells, whether respective levels, of the at least second portion of the memory cells, that represent, according to the mapping, a second plurality of transformed bits obtained by transforming the second plurality of input bits using a second transformation, are accessible from the current respective cell levels of the second at least portion of the memory cells, and (ii) only if the respective levels, of the second at least portion of the memory cells, that represent, according to the mapping, the second plurality of transformed bits obtained by transforming the second plurality of input bits using the second transformation, are accessible from the current respective cell levels of the at least second portion of the memory cells: programming the at least second portion of the memory cells to store the second plurality of transformed bits according to the mapping.