Word doc placed in Indesign gets numbered headings

This has bit me more than once, and according to Google it affects nobody else on the whole Internet. Do I feel special or what?

I write books in Microsoft Word, using Styles. Paragraph and character styles are essential for producing electronic and print books.

At random times, when I import a Word doc into Indesign for print layout, numbers appear before the headings. These numbers do not appear in the Word document. Resolving this problem drives me near to madness.

InDesign and Word both have...