If you're getting an "insufficient free space" message, your 60GB isn't really "free". Use the "fdisk" command to display the actual partition allocations.
Fedora likes to use the LVM (Logical Volume Manager). Free space within LVM partitions isn't usable by just anyone, since the software has to understand LVM as well as the filesystems with the LVM. If you're encountering problems allocating space at installation time using the Fedora graphical Disk Druid, look closely at what you're trying to set up, since the Druid will switch GUI controls on and off based on these limitations and you may be inadvertently attempting to do things somewhere other than where you think you're trying to do them.
Also, disk space accounting is a slippery subject because everyone uses different systems of measurement, plus there's overhead for the filesystem itself. So "59GB" might not actually fit within a 60 GB partition. You didn't say what the smallest allocation you tried was.
You should be able to put the Fedora 15 OS in a 20GB partition/logical volume, though.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.