Hi Airbrush,
Build it with a 12V, 500mA wall-wart, a 240 ohm reference current setting resistor, a 2.5k pot in series with a 300 ohm resistor so the minimum voltage is 2.8V for two series-connected 1.7V LEDs to be dimmed. Then the max setting of the pot will try to force the LM317's output voltage to 15,8V. But the wall-wart's output voltage will be about only 13.5V with the 400mA load, and the max output of the LM317 will be about only 12V. The pot will have a wide dead zone near its maximum setting.
Then try the 12V, 500mA wall-wart, a 150 ohm reference current setting resistor, a 1k pot in series with a 180 ohm resistor so the minimum voltage is 2.75V. Then the max setting of the pot will force the LM317's output voltage to 11.1V, and the LM317 will have adequate input voltage.
Then there won't be any dead zone of the pot at its max setting. :lol: