re: Stripping a painted piece of furniture

quote:

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The paint that's on there now was slapped on as thick as humanly possible

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Would definitely recommend stripping in lieu of sanding. THe excess paint will gum up sanding pads. Stripping is much easier than sanding IMO and will give you a better finish as you will have difficulty getting into small spaces and curves with a power sander.

As other said I would strip than use steel wool to finish then prime and paint. Would be careful with a heavy grit sand paper as you can leave marks that will require you to take excess wood to smooth out.