JPEG is a lossy compression method. Parts of the data are discarded and then interpolated when the files is decompressed. However low you have the compression set there always is some data loss. Converting to a TIFF after compressing will not reconstruct that lost data. So all you have at the end is a TIFF file with all the lost elements from the JPEG . You might as well keep the JPEG.
IF you want to have high quality files, but don't want the size overhead of a TIFF look at saving in RAW. This will be larger than a JPEG file but not as large as a TIFF. Plus there are other advantages as well. You will need special software to handle the RAW file but there is a lot of versions around, and if you have a Canon camera it comes with DPP which can handle Canon RAW files. Photoshop will also handle RAW files from most cameras, dependent on what version you have.