The most simple solution for me has been to:
1)Select the Range and copy it (ctrl+c)
2)Create a new text file (anywhere, it will be deleted soon), open the text file and then paste in the excel information (ctrl+v)
3)Now that the information in Excel is in the text file, perform a select all in the text file (ctrl+a), and then copy (ctrl+c)
4)Go to the beginning of the original range in step 1, and paste over that old information from the copy in step 3.
DONE! No more false blanks! (you can now delete the temp text file)