LSM303 Jitter

I'm trying to figure out what sort of jitter is normal for an LSM303DLHC. I'm getting a lot of jitter even using time averaging on my heading.

I'm using a breakout board from Pololu - LSM303DLHC 3D Compass and Accelerometer Carrier with Voltage Regulator.

Using the board with a 4.7uF capacitor I got the following results while the device was laying on my desk motionless (without a capacitor the values were horrible):

Heading:
Average 301.9728947
Min 300.56
Max 303.39
Variation 2.83
Averaged Heading:
Average 301.9869079
Min 301.5
Max 302.63
Variation1.13
Pitch:
Average 9.054078947
Min 8.52
Max 9.84
Variation 1.32
Roll:
Average -0.226973684
Min -0.68
Max 0.06
Variation 0.74

With only the included capacitor to the 3.3V regulator I got the following

Heading:
Average 137.3315566
Min 136.01
Max 143.6
Variation 7.59
Averaged Heading:
Average 137.3248585
Min 136.76
Max 138.33
Variation 1.57
Pitch:
Average 6.658301887
Min 2.93
Max 6.98
Variation 4.05
Roll:
Average 0.021698113
Min -1.14
Max 0.43
Variation 1.57

Any feedback on what is reasonable for jitter on a device that is sitting still?

I would suspect the constant AC hum which pervades our modern world. Did you try it away from any AC power?

Also the wires near the device (I2C?) can cause errors as it says in the datasheet:

"High current wiring effects

High current in the wiring and printed circuit trace can be culprits in causing errors in magnetic field measurements for compassing.

Conductor generated magnetic fields add to the Earth’s magnetic field, causing errors in compass heading computation.

Keep currents higher than 10 mA a few millimeters further away from the sensor IC."