24-Gauge and 26-Gauge Wire

I already have most of the components I need for my Tesla coil, like a 12kV
/ 30mA transformer, a 4"x26" secondary (the winding is actually 22"), etc. 
And I planned on wrapping the secondary with 24-gauge wire since that
seemed to be what all the guys who knew what they were doing used on that
size coil.  But it turns out I have a couple thousand feet of 26-gauge wire
handy.   Can I use this wire without any serious performance drawbacks?