LED Resistor Choice with changing voltage
An extremely simple and low cost constantish current source is shown in the circuit below. 

Q1 is initially turned on by R2.  

I_LED flowing in R1 produces a voltage per V = IR
of V = I_LED x R1
When V_R1 reaches about 0.6V Q2 is turned on and shunts base drive to Q1, thereby limiting any current increase.

ILED max ~= I_R2 x Beta_Q1  where Beta = current gain.
For say 5V and R2=1k IR2~= (5-0.6)/1k = 4.4 mA.
For Q2 Beta = 100 Imax = 440 mA - ample for most purposes.
This circuit drops a minimum of ABOUT 0.6V

Cost, size and complexity are minimal.
Results are far better than using just a series resistor.
ie Current is not "constant" but is far closer than with a resistor alone. 







simulate this circuit &ndash; Schematic created using CircuitLab



Aka:



E&amp;OE.