More power and less resistance

A while back there was a thread on what the advantages of double winding
a secondary coil would be. I got to thinking about the fact that if it
would in fact reduce the resistance of the secondary, would it also add
a little bit more power handling capability. I know that by winding a
double layer coil with both wires in parallel will reduce its resistance
by acting as one larger size conductor.

But I thought about instead of winding layer over layer, you could wind
the wires side by side. The reason I thought of winding side by side is
the fact that it would allow you to use smaller gauge wire without going
over a 1000 turns. I also thought of the fact that smaller gauge wire
such as between 20-24awg is easier and cheaper to come by.

Tell me what everyone thinks. This can definately become a reality if
its benefits out weigh a single layer larger gauge secondary.