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The strain dependence of the critical current was studied for YBCO and DyBCO coated conductors with different buffer layers on Hastelloy substrates. A maximum of Ic was observed for both the YBCO and DyBCO tapes, however the sign of the strain at the Ic peak was opposite for the two superconductors. A reversible variation of Ic with applied strain was found and the reversible strain limit was observed to depend on the buffer layer. For the IBAD-CeO2/YSZ buffered YBCO tapes, Ic recovers reversibly when the applied strain is reduced starting from 0.30%. For those with an ISD-MgO buffer layer the irreversible degradation starts at a strain less than 0.22%. The reason for this difference is discussed based on microscopic observations. Quenching occurred during V-I measurements after the applied strain exceeded 0.30%, which is close to the yield strain of the composite tape.