When we remodeled the kitchen about 8 years ago we
installed a Vent-a-Hood over the range top. The hood has
a chimney-like spacer with a 12"x12" cross-section that attaches
at the ceiling.

It is slightly out of level. Over the 42" length it drops about 3/4".
My theory is that the cause is a slight unevenness in the plaster
ceiling, either due to sag in the joists or thickness variation in the
plaster. Note that a difference of only 0.2 " over 12" will
cause 3/4" difference over the 42" length.

Several years ago, I talked the the contractor
who installed it. He proposed to carefully jack the ceiling up
from below, then go into the attic and nail in a 2x4 vertical
brace from the joists between which the hood is mounted and
a cross-piece between two rafters above. For reasons I can't
quite remember I decided against that.

Now, I'm thinking about essentially the same idea, but implemented
differently. I'm
thinking about attaching a length of fairly heavy chain by
means of lag screws to the joists, and another length to
a cross brace between the rafters above. Between the two
chains I will put a turnbuckle. Cinching up on the turnbuckle
at the low end should lift the joist just enough to level the hood.

Any opinions on the idea?

TIA

Ed