One downside to doing it this way is that the image data was decompressed and then re-compressed when it was saved. This is not a problem if your compression is lossless (just time and memory), but if you are using JPEG compression for the images inside the TIFF, you will lose quality.
There are ways to do this using libtiff directly -- I don't know of any other non-commercial tools that can do it. Basically, you need to find the TIFF directory entries in the file that relate to the image data and copy them directly into a new TIFF without decoding them and reencoding. Depending on how much you want to do, you may need to fix offsets in the entries (e.g. if you are also bringing over the meta-data)
If you are interested in being able to split, merge, remove pages from or reorder TIFF documents without losing quality (and also faster and using less memory), take a look at my company's product, DotImage, and look at the TiffDocument
class. This CodeProject article shows how to do it.