Thank you, liquidat. That was not quite what I was looking for, but it did help me figure it out. Here is what I did, which seems to have worked:
At installation, set up three partitions:
/dev/sda1: 512 Mb Ext2, mapped to /boot.
/dev/sda2: 4096 Mb unused partition, of type Linux (0x83).
/dev/sda3: Remaining space encrypted Ext4, mapped to / (file system root).
This installed Ubuntu without a swap space. After installation, I followed the instructions from Encrypted Swap Partition for 14.04 to install a randomly encrypted swap partition in /dev/sda2. I modified the commands slightly to follow the example from my 12.04 installation:
$ sudo cryptsetup -d /dev/urandom create sda2_crypt /dev/sda2
$ sudo mkswap -f /dev/mapper/sda2_crypt
Add/edit the following line to /etc/crypttab:
sda2_crypt /dev/sda2 /dev/urandom cipher=aes-cbc-essiv:sha256,size=256,swap
Add/edit the line in /etc/fstab:
/dev/mapper/sda2_crypt none swap sw 0 0