Os nad eiddo domestig yw prif breswylfa'r perchennog, gallai fod yn atebol hefyd am bremiwm y dreth gyngor ar gyfer ail gartrefi, os yw'r awdurdod lleol wedi penderfynu gwneud cais am un. Mae nifer o eithriadau statudol i bremiymau'r dreth gyngor: Mae'r rhain yn cynnwys lleiniau carafannau ac anheddau wedi'u meddiannu sy'n ddarostyngedig i amodau cynllunio penodol. Ni ellir codi premiwm ar anheddau sy'n gymwys i gael eithriad ond gellir codi'r dreth gyngor arnynt a hynny ar y gyfradd safonol o hyd.
If a domestic property is not the primary residence of the owner, it may also be liable for a council tax premium for second homes if the local authority has determined to apply one. There are a number of statutory exceptions to council tax premiums: these include occupied caravan pitches and dwellings subject to certain planning conditions. Dwellings which qualify for an exception cannot be charged a premium but can still be charged council tax at the standard rate.