I want to create an adjustable µA Constant Current source using a LM317. It is typically stated to have a 5mA to 10mA minimum current for proper regulation. The On-Semi version linked above shows a graph where this actually depends on the Vin-Vout differential. Even then, I'm looking at 2mA minimum, which is higher than the 0.1mA I am looking for. While looking at circuits of a typical regulator constant current source, I came up with an idea, and am not sure if it will work properly or not.

Since the circuit depends on Iout being shared in a series circuit, and only cares that voltage drop across R1 equals Vref (1.25V), wouldn't a second circuit, parallel to R1, allow for a greater total current draw, but still allow for voltage regulation dependent on R1? My idea (Note: RRef would be an adjustable trim pot, 12.5k just a reference value for now):

^{simulate this circuit – Schematic created using CircuitLab}

Since total Vout should be VRef + Vload, then Vout / RDummy = IDummy (For VOut 3~9 Volts, that's 10~27mA). The Led Load part should still only get 0.1mA (plus another 0.1mA from IAdj, this is okay) as desired.

##Is there any reason this would not work?##

I'm assuming if it will, then by paralleling the R2 and Led on a third circuit, that I can avoid the IAdj current as well?