You do. But because the human eye works as part peak-detector, you can get better "value" (ie efficiency) in some cases by reducing the duty cycle instead. Ie usually a LED at (IF=0.5*I, 100% duty) looks dimmer than a LED at (IF=1.0*I, 50% duty).

For example with the LTJ-811 as you have suggested, and using Fig 4 from the datasheet (which relates relative luminous intensity [RLI] vs current):

You can drive this with IF=20mA, VF~2.1V at 100% duty to get RLI~2.4, thus power per RLI unit is ~17.5mW/RLI.

You can also drive this with IF=25mA, VF~2.3V at 50% duty to get RLI~3.1*0.85~2.6, thus power is ~11.0mW/RLI.

So because dropping the duty to 50% does not give 50% reduction in perceived brightness (only 15% drop in my experience), you can use this technique to decrease power without decreasing perceived brightness.

Note that the LTJ-811 has a linear current/RLI response in the range (5mA,25mA) and I stayed in this region for this example. If you have to move out of the linear region (because you need absolute maximum brightness), then the results are going to depend on how non-linear the LED response is.