Zeners don't have to be run at a minimum current, the voltage is just somewhat lower (e.g., a 1N5242B might be 11V at 1mA, 12V at 10mA, etc.). This is true of all avalanche devices (Vz > 6V); true zeners are operationally defined by their low voltage drop (under 6V) and much softer knee (a 3.3V device might be only 2V at 1mA). For lower voltages (or more accuracy, assuming the temp range is good with it), you want a bandgap reference.
Tim