is it possible to change the order of the cols in the table whilst there is data in it. (mysql db)

ie. my table is id, col_1, col_2, col_3 and I want it to be id, col_1, col_3, col_2

I thought that I could create a new table with the cols in the correct order then copy the data across to it - but it stays in the same order! heres the code:

insert into [newtable] (id, col_1, col_3, col_2) select * from [oldtable];

Now I know that I want to specify which order using insert values etc but can't seem to figure the workaround.

By the way if it sounds a really dum thing to do - I agree but my clients wants it done and asap also