Convert ePub to MOBI with KindleGen
KindleGen is an official Amazon’s converter. KindleGen is pretty easy to use.
Run kindlegen to see all the program options.
KindleGen has an undocumented key -dont_append_source with which you can avoid storing an ePub copy within the generated MOBI file.
Another option I personally recommend to always use is -c0 which disables compression. The thing is that books converted without compression are opened by Kindle faster and turning over the pages is faster too.
So, the full command you should use is the following:
kindlegen -verbose -locale en -dont_append_source -c0 book.epub
The -verbose and -locale options are used for verbose output, so when something goes wrong it is easier to find out why.