There are a variety of simple constant current circuits (or more accurately "current limiting" circuits). These linear circuits are kind of like smart resistors that change value as the battery voltage changes. They are simpler than DC-DC converters with coils/inductors, but are not as efficient. The big advantage over the simple resistor is that they have nearly constant current (and therefore LED light output) over a wide range of battery voltage.
I don't have an easy way to draw circuits, so I googled looking for it. Didn't find the exact one, but look at
http://www.radio-electronics.com/in...urrent_limiter/transistor_current_limiter.php
Remove the stuff at the bottom of the circuit, leaving just the two resistors and 2 transistors at the top of the circuit. Once the current going through the circuit gets up to the point that the voltage across the current sense resistor gets up to 0.7V or so, it turns on the "current sense transistor". That transistor steals / bypasses the base current for the main transistor above it, thereby limiting the current.
The LED load can either be on the emitter of the main transistor (in which case the base current also flows through the load), or you can put the load in series with the collector of the main transistor (better current regulation, but you lose the 5 to 10% of current that you send down through the base).
If you don't want to use 2 transistors, replace the "current limit" transistor with two diodes. If your battery voltage is close to the LED voltage, then put the LED in series with the collector of the transistor.
If you have lots of excess voltage, then put the LED off to the right of the junction of current sense resistor and the current limit transistor emitter.