Keep in mind that a rear brake is almost always "squishier" than a front due to the extra length of housing.

As DannoXYZ said, examine the cable housing, but not just externally. A bad end cut with a burr will cause spongy brakes. These can be spotted if the housing moves slightly sideways when the lever is pulled. Filing or grinding the ends flat will fix it.

I'd also take a hard look at the routing. Remove any excess and make the runs as smooth and flowing as possible. Sharp bends allow the flat-wound housing to expand, and when pulled will compress again.

Although you should never use STI housing for brakes, there is a "linear" housing made for BMX bikes that is also flat-wound and gives much less compression.