But I didn't remove the sunflower after all; I decided that it was too nice a decoration to remove.
Instead, I put the bird trimming on the opposite side.
So now, I can wear my hat four different ways:
1: Sunflower in front, bird in back, sides untrimmed.
2: Bird in front, sunflower in back, sides untrimmed.
3: Sunflower on right, bird on left, front and back untrimmed.
4: Bird on right, sunflower on left, front and back untrimmed.