Measuring current draw of pedals

[sfr]

Looking to make an integrated, all-in-one pedal board, I sat down and measured out the current draw of the pedals I use frequently, so I can figure out how I want to power the thing. 

The interesting part is that several pedals draw considerably more power when I turn them on than in bypass.  My Octavia actually seems to be the worse offender in this case. 

Is this extra current draw the result of the LEDs being turned on, and that's it?  Or, considering I often ground the input to board when in bypass, do the circuits themselves draw more current when they're being used?   

Also, should I be running an input signal when I'm measuring the current draw, or will that not change anything? 

[Seljer]

I think the LEDs really draw a lot if you're running them bright, espescially on circuits that barely use anything alone (most fuzz/distortion and EQ circuits)