About a third of the exterior of my house is very rough stucco wall. Thick
nap rollers are necessary to get into the nooks and crannies of the stucco.
The rollers splatter a lot of paint everywhere and require a lot of elbow
grease. I have been using those little 50 cent disposable foam brushes for
some of the finer work (near trim). It occurred to me to try a large foam
sponge.

Has anyone tried such an approach?

Does anyone have a better suggestion?

About a third of the exterior of my house is very rough stucco wall.

Does anyone have a better suggestion?

Rent a sprayer from Home Depot

"Rudy" wrote
About a third of the exterior of my house is very rough stucco wall.

Does anyone have a better suggestion?

Rent a sprayer from Home Depot

Folks here warned me away from a sprayer a couple of months ago. Too much
splatter, and so masking, required.

I tried an enormous foam rubber sponge from the car cleaning supplies
department of Wal-Mart. A buck each. Works better than the thick-napped
roller. I went through five of them for half the house.