The key thing is to make sure that Calibre converts them as [EBOK] mobi files instead of [PDOC] mobile files. So...
1. Launch Calibre, and then load the MOBI file to your library via the "Add books" button at the top left of the navigation bar.
2. Select the book from the title list and click "Convert books" from the top nav bar. Make sure at top that "Mobi" is selected in both the "Input format" and "Output format" dropdowns. (Or whatever source you're converting from)
3. A Convert dialog box will open. Click "MOBI Output" in the lefthand pane.
4. In the "Mobi file type" dropdown, choose "both" to ensure compatibility with both newer and older Kindle devices. In the "Personal Doc tag" field, change "[PDOC]" to "[EBOK]" (this is what controls the destination directory on the Kindle).
5. Click OK, and Calibre will convert and output a fresh MOBI. Sideload this to the Kindle as usual, and it should show up in the Books list instead of the Docs list on your device.
One upside to this [EBOC] format is that it will also give you page numbers on your display. Albeit I think the original page numbers in the book - not actual pages on your Kindle.
