Win XP SP3 needs SP1 or SP2

I got an old laptop back from the dead by installing Windows XP on it. It had a corrupt filesystem so pretty much nothing on it was usable. After getting Windows XP (no Service Packs) running from the restore/recovery disks, I got the setup of Windows XP Service Pack 3 and tried installing it. The setup complained with the error message indicating that it needed at least Service Pack 1 installed. Now, I didn't have Service Pack 1 or Service Pack 2 around because all my computers have restore/recovery CDs that already have SP2 so I got a copy off the Internet. I decided to leave the SP3 installation to another day as I was getting late to work, but was wondering - aren't service packs supposed to be cumulative?