I connected with FF 3.6 to that website and sniffed the connection with Wireshark. Indeed, the first SSL connection attempt sends an TLS1.0 client hello and the server responds with a handshake failure, then FF3.6 immediately retries using the SSLv2 compatible hello which succeeds. All this happens transparently to the user so you don't notice the initial failure. Try setting the system property https.protocols
to SSLv2Hello
. Note that the JSSE does not support SSL v2, this is just the format of the initial client hello.
EDIT:
Well, never mind, I see that JSSE uses by default the SSLv2 client hello. I don't know why the first connection attempt failed. Maybe you just have to try twice in a row.