Hi David,
please provide your wM version with Fix Level.
Provide the current value for watt.net.useJSSE as TLS v1.1 and TLS v1.2 are only available when running on Java 7 and newer and have useJSSE set to true.
Check in Empower for KB article related to POODLE to see if your wM version can handle this and which Fixes are required for that.
During TLS Handschake the server and the client should start with TLS v1.2, and if this does not succeed, then going down to TLS v1.1 and finally TLS v1.0.
Looks like the Server is not accepting the TLS v1.0 any longer when you are the client or vice versa.
Additionally you should set strongCipherOnly to true for more security.
Regards,
Holger
#Integration-Server-and-ESB#webMethods#webMethods-General