Without proper preparation, wallpaper will not adhere properly to a wall. This is particularly true with newer, pre-pasted wallpaper that doesn't rely on the heavy-duty adhesives of old. If you put up wallpaper and notice that the sides aren't sticking or are peeling back, you can fix this problem and prevent it from recurring.
Prepping the Area
Walls must be properly prepared for wallpaper -- even the new pre-pasted kind. This is particularly true if the walls have a special painting technique applied to them. Sanding down paint to roughen the surface will give the adhesive something on which to stick. Tinted or glazed walls are very slick and the adhesive won't create a good bond with this type of surface. Use a medium grade sandpaper to rough up the surface.
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What to Try First
Before taking down the wallpaper and starting over, there are a few things you can try. First, sand down the wall under the areas where the wallpaper isn't sticking. Brush off the dust and vacuum it up. Pieces of dust will also interfere with the adhesion process. Use a spray bottle and dampen the underside of the wallpaper. Press it firmly into place. Lean something heavy against the corner to hold it into place until the adhesive can cure.
Re-Adhering the Wallpaper
Try an actual wallpaper adhesive. Test it in a small, inconspicuous spot. Some adhesives may bleed through the paper, causing ugly marks and blotches. Once you've tested it, run a bead of adhesive down the corner of the wall. Press the wallpaper into the adhesive and smooth it out. Remove any adhesive that squeezes out from under the paper with a putty knife.
Getting Rid of Bubbles
Improperly installed wallpaper can also fail to adhere properly. When you're installing it, it's vital to smooth out your work as you go. If you don't, bubbles will appear under the paper. Over time, the edges will come up. Use a squeegee or even a rolling pin to smooth out each panel of wallpaper as you install it. This will remove the air bubbles and give the adhesive a firm grip on the wall.