A reversible strain effect on transport critical current I c was found in Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) high-temperature superconducting round wires. I c showed unambiguous reversibility at 4 K and 16 T up to an irreversible strain limit of about 0.3 % in longitudinal tension, prompting hope that the Bi-2212 conductor has the potential to sustain mechanical strains generated in high-field magnets. However, I c was not reversible under longitudinal compression and buckling of Bi-2212 grain colonies was identified as the main reason. A two-component model was proposed, which suggests the presence of mechanically weak and strong Bi-2212 components within the wire filaments. Porosity embedded in the weak component renders it structurally unsupported and, therefore, makes it prone to cracking under strain ε. I c (ε) is irreversible in tension if the weak component contributes to the transport critical current but becomes reversible once connectivity of the weak component is broken through strain increase or cycling. A modified descriptive strain model was also developed, which illustrates the effect of strain in the Bi-2212 conductor and supersedes the existing descriptive model. Unlike the latter, the new model suggests that higher pre-compressive strains should improve I c if buckling of Bi-2212 grains does not occur, and should result in a wider I c (ε) plateau in the applied tensile regime without degradation of the initial I c. The new model postulates that a reversible strain effect should exist even in the applied compressive strain regime if buckling of Bi-2212 grains could be prevented through elimination of porosity and mechanical reinforcement of the wire.