The　circumference　of　a　graph　is　the　length　of　its　longest　cycles.　Jackson　established　a　conjecture　of　Bondy　by　showing　that　the　circumference　of　a　3-connected　cubic　graph　of　order　n　is　Ω(n0.694).　Bilinski　et　al.　improved　this　lower　bound　to　Ω(n0.753)　by　studying　large　Eulerian　subgraphs　in　3-edge-connected　graphs.　In　this　paper,　we　further　improve　this　lower　bound　to　Ω(n0.8).　This　is　done　by　considering　certain　2-connected　cubic　graphs,　finding　cycles　through　two　given　edges,　and　distinguishing　the　cases　according　to　whether　or　not　these　edges　are　adjacent.　©　2017　Elsevier　Inc.