How to backup contacts only in iCloud?

I have a corrupt backup so restoring my phone from a previous backup isn't an option for me. All I want to do is backup my contacts and notes to iCloud and wipe everything else clean to get rid of the corrupted files. I'm currently using the most recent iOS 8.3. Please help! I'm going crazy here! Whatever is corrupted on my phone is preventing me from making phone calls longer than 5-10 seconds long...it drops calls every couple seconds. ugh!