Coupled enrichments in ¹⁸⁶Os/¹⁸⁸Os and ¹⁸⁷Os/¹⁸⁸Os in some ocean island basalts have been interpreted to reflect material transfer from Earth's outer core to the base of the mantle. The outer core is a viable source for these coupled enrichments if it is able to maintain sufficiently high Pt/Os and Re/Os ratios for sufficient time. Iron meteorite studies and some experimental data indicate that progressive crystallization of the inner core is a plausible mechanism for generating the required high Pt/Os and Re/Os ratios in the outer core. However, the conditions of the experiments and meteorite parent bodies are far different from those in Earth's core, particularly in terms of pressure. Here we present experimental results on the partitioning of Os, Re and Pt between solid iron and liquid iron sulfide solutions over a wide range of pressures, from 3.3 to 22 GPa. The solid/liquid partition coefficients for these elements decrease, and become more similar to each other, as pressure increases. This behavior is consistent with an increasing misfit of each element in the iron lattice with increasing pressure, due to the small compressibility of Os, Re and Pt relative to iron. The partition coefficients, and differences among them, are too small at the conditions of these experiments to generate the radiogenic Os isotope anomalies observed in some plume-derived lavas. At 22 GPa the partition coefficients are such that inner core crystallization elevates the Pt/Os ratio of the outer core by only 11%, and the Re/Os ratio by only 6%; after 4.5 Gyr, the calculated ¹⁸⁶Os/¹⁸⁸Os ratio of the outer core is only 0.0012% higher than it would be in the absence of inner core crystallization, and the ¹⁸⁷Os/¹⁸⁸Os ratio is only 1.4% higher. If the pressure effect is due to lattice strain, the partition coefficients are expected to decrease further at the pressure and temperature conditions relevant to Earth's core. Thus, the present data set does not support the idea that radiogenic Os isotope anomalies originate in the outer core.