My first suggestion is: use some other material.
I have to admit bias: balsa is one of my two absolute un-favorite modeling materials. (The other is lead.) Balsa has exactly two virtues that may - may - be of interest to modelers: it's widely available, and it weighs amazingly little. If you're building a flying model airplane, that weight factor will be enormously important to you; in fact it's likely that nothing but balsa will do the job. But for virtually any other type of modeling, balsa is just about the worst possible choice. It has a coarse grain, breaks easily, crumbles under all by the sharpest cutting tools, and soaks up finishing materials like a sponge.
I should note one additional good quality of balsa: it's amazingly strong for its weight. Quite a few years ago I helped my stepdaughter with a middle school science fair project. (The teacher said she could get as much help as she wanted. Heh heh heh!) The assignment was to make a balsa wood tower, at least a foot tall and weighing no more than two grams - made of components no longer than six inches. The competition was to see how much weight the tower could support before it collapsed. For that purpose a plastic bucket was suspended from the top of it, and the students shoveled sand (by the tablespoon) into the bucket until the tower crashed. After my stepdaughter put eighteen pounds in her bucket, the judges told her to quit. Score one of those rare victories for Stepdad.
But unless you're building a project for a science fair, or building a flying airplane, you'll have much better luck with some other material. Would sheet styrene be a possibility? If it has to be wood, try basswood (the second most common wood in hobby and craft stores). Better yet, if you have a store in your community that sells veneers, check out what it has to offer. (Some veneers are specially treated to be super-flexible.)
My personal favorite modeling subject is sailing ships. When a newcomer to that hobby asks me for suggestions, the first one I offer is, "wipe from your mind all recollection of balsa wood."
If you can be a bit more specific about your model, we probably can offer some better ideas. Good luck.