The characteristic that gives a knockdown texture its name is the flattened appearance it gets after you've lightly knocked it down with a drywall knife. You can't knock down wall texture, though, until you've gotten some on the wall, and a paint roller is a convenient tool for this part of the job. The most useful rollers for texturing are made of coarse vinyl or coconut fibers and are intended for applying texture paint.
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Wall textures add visual and tactile qualities that can make a room seem smaller and more accessible, since some textures are highly stylized. Knockdown is one of the more basic texture styles, though; it's easy to do and doesn't require much texture material. To accomplish a knockdown, you apply texture -- often the same joint compound you used for taping -- by scraping it on with a drywall knife or rolling it with a texture roller. After the texture stiffens a bit, flatten it by running a drywall blade over it.
Texturing With a Roller
You can apply many types of wall texture with a paint roller. Some are so thin that they resemble a heavy coat of paint; these you can apply them with a medium-nap roller cover. To apply a knockdown, though, you need stiff texture and a stiff roller cover, because you want the material to form clumps on the wall. Most paint outlets sell texture roller covers, which are primarily intended for applying texture paint. Use one of these to apply knockdown texture.
Mixing and Spreading the Texture
Most drywall pros make wall texture from regular joint compound, and you can easily adapt this versatile material to make a rollable knockdown texture. Transfer enough pre-mixed joint compound for the job to a 5-gallon bucket and thin it by adding water; stir it until it has the consistency of honey. Pour some into a rolling pan and apply it to the wall or ceiling with a paint roller fitted with a texture cover, using very light pressure. The trick to leaving clumps that you can knock down is to avoid overloading the roller and to use light pressure when rolling.
Putting the "Knockdown" in Knockdown
A texture doesn't become a knockdown until you flatten it -- usually with a drywall knife. The texture needs to stiffen for about an hour after you apply it, or you might remove it completely during this part of the procedure. Hold the drywall knife so that its blade is almost flat with respect to the wall and run it lightly over the texture. The direction you run the knife matters, because the knockdown pattern follows it, so it's best to maintain the same direction when knocking down a wall or ceiling. Sanding usually isn't necessary after knocking down the texture -- just prime and paint.