Because of this, it is usually helpful to include information about MOV file content when posting questions like yours. This means it can contain any form of compressed data compatible with the system on which the file was originally created-from text and/or still images to various forms of compressed audio and/or video data. To begin with, the MOV file extension refers to the file container and not the compression formats contained within the file container. (I.e., File Size = Total File Data Rate x Duration of the Video Clip) Unfortunately, the best way to do this is dependent on how the source file was made and your specific requirements for using the final modified file-neither of which were indicated in your original posting.
The simple answer is to make the combined total data rate of the new file less than the combined total data rate of the source file.