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Correct, but for a website, you should probably disable DHE and other legacy ciphers. DHE is only useful for a website to support Internet Explorer when using RSA certificates since it only supports ECDHE with ECSDA certificates. Use ECDSA certificate and ECDHE works fine for it.
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Our solution to that email server issue is disabling support for unencrypted connections. That's obviously not something most people would accept since they would be concerned about missing emails. For us, we're more than happy to reject mail from broken / insecure mail servers.
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