Daft question about double bridles

[Roxylola]

So I invested in a double bridle for supercob which arrived today. I'm so used to monocrown headpieces and this one isn't.
So at the moment all the buckles are on the left, the noseband, the slip head etc. It looks really uneven to my mind, and I want to swap the slip head so that it fastens on the right. Is there any reason I can't/shouldn't?
Sorry for being such a noob, I promise I'm not totally incompetent really

 

[milliepops]

it should be swapped round.
Noseband fasten on the near side, sliphead on the off side.

 

[Roxylola]

I thought that was right, it looks so cluttered otherwise