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A sagging couch could be the result of worn out cushions, old springs, or a bad frame. If the problem is the cushions, you're in for an easy fix. If the cushions seem fine upon inspection, you may have to replace the springs or the frame. Depending on the level of damage you may need to replace the entire couch. Before you start taking your couch apart, take some pictures so you have something to refer to. If you can, take the pictures to a local furniture repair shop and see if they can help you determine the problem. Remove all the sofa cushions and turn the couch over so that you can see the bottom. Look for torn fabric and broken or rotted wood.  If you see any cracked wood, or wood that is "bowed" out, you'll need to replace it. This will involve taking off most of the upholstery fabric and can be time consuming.  You may have to remove some of the fabric on the bottom, known as a dust cover, to inspect the springs. Be gentle and take care not to rip the fabric. Some couches have zig-zag springs which are also known as "sagless" springs. Other couches use coiled springs.  Determine whether your springs are bent or broken. If the springs are bent you may be able to fix them yourself. If they're broken you may need to bring your couch to an upholsterer. Older couches tend to have coiled springs, while newer couches have zig-zag springs. Your couch may not have springs at all, depending on the quality of the frame. Check the space beneath the cushions. You may find that the slats or straps of the couch have snapped.
Determine why your couch is sagging. Take pictures. Inspect the frame of the sofa. Take note of what kind of springs your couch has.