As mentioned in one of the comments, this:
If the correct current is on an LED but the voltage is too high
... is not possible.
If the current is "correct", then the voltage will be equal to the characteristic voltage of the diode.
simulate this circuit – Schematic created using CircuitLab
In the above schematic,
Vdiode will be about 1.9V, because 10kV/1MΩ is about 10mA, and that's the voltage this particular LED arrives at if biased on by 10mA (datasheet PDF).
Were you to change the value of
R1 to 1 ohm, then approximately 10kA would briefly flow through the LED, resulting it a burned-out LED.
A key concept to grok is the difference between Constant Current and Constant Voltage regulators. A typical "bench" power supply is Constant Voltage, meaning it puts out X volts at some current, and will regulate its output to remain at X volts whatever its load. Diodes approximate Constant Current regulators to a degree, because you can think of the voltage being dependent upon the current.