And, for the love of God, don't use much compressed air.
I grenaded a fan by overspeeding it; itty bitty little plastic fan blades fell out.
HP didn't sell the fan unit- their fix was to sell me a refurb PC for more than I bought the new PC for.
I Mickey-moused a similar fan installation, but it never ran the same again.

For the mini-tower, I poke a chopstick in the stopped fan, then used compressed air.
That still doesn't get off the dust stuck to the blades.
Sometimes I use a small paintbrush or Q-tip on those.