We determined high-pressure melting curves for Fe 3C, Fe 7C 3 and the Fe–Fe 3C eutectic using laser-heated diamond anvil cell techniques. The principal criterion for melting is the observation of plateaus in the temperature vs. laser power function, which is an expected behavior at isobaric invariant points (e.g. congruent, eutectic, or peritectic melting) as increased power provides the latent heat of melting. We verified this technique by reproducing the melting curves of well-studied congruently melting compounds at high pressure (Fe, Pt, FeS, Pb), and by comparison with melting determinations made using thermocouple-based large-volume press techniques. The incongruent melting curve of Fe 3C measured to 70 GPa has an apparent change in slope at ~ 8 GPa, which we attribute to stabilization of Fe 7C 3 at the solidus and the creation of a P– T invariant point. We observe that Fe 7C 3 melts at higher temperatures than Fe 3C between 14 and 52 GPa and has a steep P– T slope, and on this basis predicts an expanding field of Fe 7C 3 + liquid with pressure. The Fe–Fe 3C eutectic melting curve measured to 70 GPa agrees closely with multi-anvil data and thermodynamic calculations. We also measured the eutectic composition as a function of pressure using an in situ X-radiographic imaging technique, and find a rapid drop in carbon in the eutectic composition above about 20 GPa, generally consistent with previous thermodynamic calculations, and predict that the eutectic lies close to pure iron by ~ 50 GPa. We use these observations to extrapolate phase relations to core-relevant pressures. Convergence of the Fe 3C and Fe–Fe 3C eutectic melting curves indicate that Fe 3C is replaced at the solidus by Fe 7C 3 at ~ 120 GPa, forming another P– T invariant point and a new eutectic between Fe and Fe 7C 3. Thus, Fe 3C is unlikely to be an important crystallizing phase at core conditions, whereas Fe 7C 3 could become an important crystallizing phase.