GIF and PNG-8^* don't support alpha transparency. Each pixel either needs to be completely transparent or opaque, no partial transparency—so your <1% opacity won't work.

You have a few options:

1. Use PNG-24, which supports full alpha transparency. If you need to you can then use a third party tool (such as CompressPNG or TinyPNG) to convert to PNG-8 and retain the alpha transparency.

2. Make the areas completely transparent. You can either modify your original artwork or map a color to transparency in the Save for Web dialog (as seen in this Q&A).

3. If you are using a recent version of Photoshop (CC) you can use the new export (File → Export → Export As), which (as far as I know, I don't actually have CC to check)does support full alpha transparency with PNG-8.

^* This isn't a limitation in the PNG format but Photoshop's Save for Web feature.

GIF and PNG-8^* don't support alpha transparency. Each pixel either needs to be completely transparent or opaque, no partial transparency—so your <1% opacity won't work.

You have a few options:

1. Use PNG-24, which supports full alpha transparency. If you need to you can then use a third party tool (such as CompressPNG or TinyPNG) to convert to PNG-8 and retain the alpha transparency.

2. Make the areas completely transparent. You can either modify your original artwork or map a color to transparency in the Save for Web dialog (as seen in this Q&A).

3. If you are using a recent version of Photoshop (CC) you can use the new export (File → Export → Export As), which (as far as I know, I don't actually have CC to check)does support full alpha transparency with PNG-8.

^* This isn't a limitation in the PNG format but Photoshop's Save for Web feature.