PWMming high powered leds smoothly

By the way I ended up modifying the pwm code as follows and got a very nice non linear dim:

if (_interval<=_pwmIntervals){
    _interval++;
    _auto_power=pow(_logxfactor,(_interval/_R))-1;
    auto_power=255-(_auto_power*(power_percentage/100));
    analogWrite(led,auto_power); 
}

Here are the results of the code plotted on a graph (I got the idea of doing this somewhere in this forum and would recommend it to anyone implementing their own dimming ).

Very informative guide here(Redirecting…) and also where the above code comes from.

Now I am facing one problem, however, and that is that at very low levels (the first 8 steps) the 'steps' are very conspicuous so I would like to find a way to smoothen that out. Would that mean increasing the resolution of the arduino pwm?