Just like when importing Word documents, you can select what stylesheets and attributes to bring into the InDesign or InCopy document, add the same options dialogue window when importing InCopy documents into InDesign. Oftentimes the writer of the InCopy story doesn't use the same stylesheets as the InDesign document. In my case, I build newspapers and we are constantly improving the design and simplifying the naming process for stylesheets. The reporters forget to use the template and therefore old styles or misnamed styles get brought into the document. There are ways around this of course, but when I need to import 50-80 stories and format them within 4 hours, it's a pain.