Too low won't hurt it, and most LEDs are rated for "pulse" modulation for higher output situations... for instance a Cree XR-E is rated (from memory, correct me if I'm wrong) for 1.8amp operation at 10% of a 1khz cycle.
If you want to dim them, 2 chioces are "lower power" or "pulse" modulation...
Pros/cons...
Lower power -
Pros: Simple (stick in a resistor/take out some current, etc...), cheap, LEDs are more efficient at lower powers (to their Vf cutoff point).
Cons : Wasteful... a 20mA rated LED (or a larger LED/array for better comparison), at 10mA uses 1/2 the power of it's rated output. (Sounds good, but see below)...
"Pulse" modulated LED
Pros : Extremely efficient,
--if a 1000khz frequency at 10% duty cycle is used, at rated 20mA current, the LED (stationary) will "look" the same to the eye as a full 20mA LED, but using only 1/10th the power. Eyes cannot easily detect frequencies above around 100hz from a stationary source. If source is moving, "flicker" can be detected, frequency and duty cycle can be tweaked further to make this undetectable.
-- Using lower power input, (10mA), combined with a "visually stable" pulse (say 500hz/20% duty cycle), the LED would appear roughly identical to a 10mA constant, but using only 1/5 the power (or 2.0mA effective).
-- Using 20mA input, 1000khz, at a smaller duty cycle (5%), the eye might see a drop in output... tweak as desired for "50% dim", etc). Your lower limit is the speed of the LED itself (Off-On-Off cycle time, typically in the 10 nanosecond to 1 microsecond range)
Cons:
Cost of circuits - ($$)
Cost of circuits - power to run the circuit
Space required for circuits
Tweaking to eliminate "flicker"