I used a system called Ceiling Max in a basement bathroom and hall
It lets you use regular suspended ceiling tile (I used 2 x 2) but they
are mounted right against the bottom of the joists and can still be
removed from below.
It won't work if you have anything likes pipes running below the
joists, and is a little fussy to install because you have to shim the
mounting strips to be even or the ceiling will look wavy. But I am
happy with the result. In my area, both Home Depot and Lowes carry the
standard pieces. I had to order a few special items direct.
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I had a similar problem in my house and went with the 2X2 ceiling tiles. They
require 3 1/2 inches below joists in order to facilitate removal.I ignored this
suggestion and put it only two inches below and can easily remove tiles when
the need arises. The rason you are having trouble with the staple 12X12 type is
mositure. The moisture normally found in a basement raises havoc with those.
Also try to find aluminum tracks for the suspended ceilings as the steel ones
will rust in high moisture areas.