What would you recommend as a good speaker. Just saying to upgrade is not much help.
3db mentioned a big factor with efficiency, probably the most important given the Cayin's limited power. Most pp tube amps like the Cayin have pretty low output impedances compared to their SET cousins, which require conscientious attention to speaker matching; pp amps usually play nice with most speakers.
I've heard the Cayin's bigger brother, the 70T I think it was. No offense to Cayin fans, but it sounded like an average to mediocre push/pull tube amp. To these jaded ears, good tube pp amps, which the Cayin certainly was not, sound pretty much like ss power, and they're soooo expensive relatively speaking they aren't worth the trouble.