Making a beacon indicator LED burn its brightest without burning out

[DanL]

I'd like to put an indicator LED onto my beacon, but I want it to burn its brightest. Yes, yes... the easy way would be to put it between the +battery and ground pins. I want it to put it in so its power is modulated, though... partly to learn more about the calculations involved in PWM signals, and partly for the cool strobe effect when moving the beacon quickly ;-) The problem is, because the power for the LED is modulated, the LED is going to be perceived as dimmer than it would be unmodulated.

Lets say we have an LED with a 3.5V drop that takes 20ma. How could I calculate the resistor to make the LED appear the brightest? Specifically, rather than using 7.2V (or whatever your battery is at) for your resistor calculation, can you use some kind of 'perceived voltage' that can be calculated when the frequency of the modulation is known?

I guess what I'm basically asking is does the LED act as if its power input is a modulated 7.2V minus drop-across-resistor (what it actually is), or does it act as if its power input is a constant 'percieved-voltage' minus drop-across-resistor. If the latter, can you safely 'overclock' the LED by using resistor with a lower resistance than you normally would use to make it appear as bright as it does when its power is unmodulated?