System and method for programming cells in non-volatile integrated memory devices

In a non-volatile memory including an array of multi-state storage elements connected in one or more columns along bit lines and along one or more rows connected to word lines, a method of programming one or more selected storage elements along a first word line each to a corresponding target one of said multi-states during a programming process, comprising:

• applying a set of voltages to program the selected storage elements each to a corresponding target one of said multi-states by programming circuitry connectable to the bit lines and the word lines, the set of voltages including a series of one or more programming pulses applied to the first word line;
• and
• prior to applying the first of the programming pulses, limiting the current through the bit lines by circuitry connectable to said bit lines, whereby the current through a first of the selected storage elements is limited to not exceed a value dependent upon the first selected storage element's corresponding target state during the programming process, said value being set independently of the current limit value of the other bit lines.