Depending on the care with which the varnish was applied, you will have a surface that is top sealed, penetrate-sealed, patchy, cracked, peeled and possibly even weathered.
I can understand why, when remodeling or updating the doors and door trim in an older home, why you might want to apply latex paint over varnish.
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Preparation Is All
As it is often stated here on this website, preparation is all.
Prepare the job well, and you will have success.
Shortcuts on the preparation could mean short circuit of satisfaction in look and longevity.
Scrape all loose varnish, and test what appears to be well-adhered varnish to make sure it is.
If you paint over loose varnish, when the varnish comes off, and it will, the paint comes with it.
This is nothing to do with the paint quality, and everything to do with poor preparation.
Sand the entire varnished surface to eliminate any glossy spots and to smooth the wood. I would use a #150 grit sandpaper.
If there are holes or voids to be filled, and since you are now coating the varnish with an opaque latex, now is the time to fix that damage since a patch won’t show through the paint as it would through clear varnish.
You can use a wood filler or spackling compound, both normally available at your professional paint store.
Read the application directions on the containers for help in selecting the best product for your wood-fill project, for application instructions, and to make sure you wait the necessary drying time before coating.
When the filling is done, sand it smooth.
Wipe the entire area with a slightly dampened cloth to remove all dust. Wait for it to dry entirely.
Even though you have sanded the previously varnished wood, unless you were able to remove the varnish entirely, you will be coating over an alkyd or urethane (usually) when you paint.
Visit the professional paint store and ask them for a good quality, waterborne, transition primer.
Tell them you want one so that you can apply latex paint over varnish. You want one that will bite into any existing alkyd or urethane, and provide a uniform base for the colored topcoat.
After application of the transition primer via brush, roller or sprayer, you might need to do a gentle sanding to smooth out the finish. If you do so, damp-wipe the project when done, and wait for it to dry.
If it is a door and door trim that you are painting, it is normal for folks to select a semi-gloss finish. The semi-gloss will differentiate itself from the wall paint, which is often a flat, matte or eggshell finish, providing a bit of contrast.
More importantly, the historical belief is that a glossier finish will impart better cleaning resistance, as door frames and doors often get finger marks that have to be washed regularly.
If you are buying a mid-to-low quality paint, then yes, opt for the semi-gloss sheen.
Lower cost paints do not resist cleaning very well, and burnishing is often the result.
On the other hand, if you select some of the more modern, 100% acrylic, formulated-for-cleaning-resistance paints, use whatever sheen you want, as they are built to resist normal cleaning.
Read the instructions on the paint can first!
Then brush, roll or spray as directed.
When painting the trim, I would opt for a “whiz roller” and do a final roll from floor to top of the door, across the top, then from floor to top of the door on the other side, to ensure I didn’t leave brush marks.
When rolling the door, after applying paint to the entire surface, back-roll from floor to ceiling to eliminate roll marks, and thicker paint which often occurs as the edge of the roller moves up the wall.
Do not wait too long before back rolling as doing so when the paint is almost dry may add more marks than it erases.
Sit back and enjoy!