Leveling floor for laminate install
 

I'm trying to level a room in preparation for the installation of
laminate flooring. The laminate flooring requires the subfloor to be
flat to 1/10" over 4'. The room is 17' x 12' and the walls are
supported by the foundation footing. There are two joists running
parallel to the 17' wall that are 4' apart. The joists are 4" x 6"
beams and the subfloor is 3/4" plywood.

The problem is the two joists are 1/4" lower than the walls. The 1/4"
drop is constant along the majority of the room and reduces a bit as
the joists approach the end of the room. The two joists are level with
each-other.

We have considered the following options to level the floor:

1. Lay 1/4" hardibacker between the joists down the length of the room
and screw them in place. Level remainder of the floors to the wall
using quicklevel cement.

2. Raise the joists by adding a 1/4" shim at the top of the piers.

We are thinking of going with option 1 because we aren't comfortable
performing option 2. We are worried we don't have the skills and we
may cause damage. In addition, we don't know where to get a jack to
lift the beam the 1/4".

Any suggestions on how to proceed with option 1? We ran a test run
with the leveling compound with mixed results. The leveler doesn't
appear be 1/4" thick (still drying).