You MIGHT have to do a little sanding if any of the wood has turned gray. It's my understanding that wood adheres best to paint that has a smooth unweathered appearance.

My preference is to do a first round of striping with heat and then go with a chemical stripper. Getting the bulk of the paint off before the chemical step lessens the "messiness" of the chemical stripping.

I like the new soy based strippers but there are lot of options out there these days

Diane

I'm still trying to find the best way to go. Started with heat and may left it on too long - it looks like it burned a section of the wood. Then tried the soy based stripper, but removing it from the vanes of the shutters is not going well.

I'm not sure what all the fuss is about? Is the paint peeling badly? Do you plan on using the slats to adjust light or air? If not, I'd just scrape where needed, sand a bit, and add a new coat of paint, and repair where necessary. About the only way to get the slats done properly is to disassemble the shutter--which is a complicated and frustrating task.

The shutters are original to the 90 year old house and have four coats of paint on them. The top layer - black - was slathered on thickly and is cracking in a lot of places.

With lead paint under there somewhere, I don't want to scrape and sand. If I were to paint over the black, I would have to prime then paint, so that would make it six coats of paint. And I would still be risking that the black paint left behind might peel later.

It's slow going now because I'm still experimenting, but I hope to pick up speed once I figure out the best way to do this.

With drop cloths, scraping is tedious, but the safest way to remove lead paint--and you don't need to go down to bare wood, since no children can reach them to chew on the edges.
If the black is less than thirty years old, then it's not lead, so I'd scrape off that layer to sound paint, then add a new coat; black is popular, but another original color is a very dark green-nearly black looking.
In the end, scraping will be the best method I'd use.

Unless your house is historically significant or local codes dictate what you can and can't put on your house, I would just replace them. As you are finding out this a very labor intensive job, not to mention you risk compromising your health using that heat gun. Shutters can be had in Al , vinyl and wood. Or better yet build them yourself

Before you do anything, I'd check out the page I've linked here--it gives every sort of information about shutters, their history and how to do it right.
A big mistake would be to replace your shutters with aluminum ones, or to get just anyone to put them up--they must be placed right to look good, and most people today believe they should be mounted outside the window casing, exposing all of the trim--historically and aesthetically wrong, and it will make even real shutters look like cheap imitations.
The site I linked to has pages on windows, restoration and all sorts of great information on old houses in general.

Here is a link that might be useful: Old House Guy Shutters

Speedheater Infrared Paint Removers and the Boomerang Scraper from www.eco-strip.com work well to loosen paint under the louvers and more easily scraper it away with scraper blades that can get under there.