You remembered that one! Even I had to think a while.

Falling Birds would a good band name. Though I think the band would play only melancholic music because Falling Birds sounds a bit ghastly and sad. "Biiiiiiiiiiirds faaaaaaaaaaalling. Froooooooooom theeeeeee skyyyyyyyyy! Oooooooooh nooooooooooo!" A whole long play album full of sad stories of birds falling. All but one. The last song, perhaps the bonus song, would be the birds cheerfully singing and the band translating: "Gotcha! We jump and open wings at the last moment so we don't go all splat on the ground." It could be like a children's song:
"All the birds birds birds
Tuck their wings wings wings
And they jump jump jump
In the air air air
And they fall fall fall
Towards the ground ground ground
Then they open their wings and fly away-way-way."