How can I remove a Host entry from an ssh config file?

The standard format of the file is:

Host example
  HostName example.com
  Port 2222
Host example2
  Hostname two.example.com

Host three.example.com
  Port 4444

Knowing the host's short name, I want to remove an entire entry in order to re-add it with new details.

The closest I have got is this, except I need to keep the following Host declaration and the second search term will capture two many terms (like HostName):

sed '/Host example/,/\nHost/d'