You can implement churge pump converter, such as LM2623 (**broken link removed** ), generate 4*1.6V=6.4V of 3V with >90% efficiency and supply all 4 LEDs connected in series (3mA current) of this 6.4V ..
check out supertex or maxim. there are many chips out there for current regulation as they current devices. you can use a resistor but there is no compensation for input voltages swings.