Winzip has three modes of compression, the default mode is the middle one, if you select maximum compression this may compress the file sufficiently for your needs, failing that you have other option's depending on the file type.
For example, if it was a bitmap (picture), you may have already tried converting it to JPG, but as you have found to get the required compression may result in quality loss. I resolve the loss of quality by using MS Photo Editor, which is part of the office suites. Save the file as PNG.
Why not tell us what type of file you are trying to compress, are you also confident in MS DOS mode?