We present new experimental partitioning data for a range of petrogenetically important elements at pressures of up to 3.4 GPa. The experiments are designed to mimic low degrees of anhydrous melting beneath mid-ocean ridges. The available data indicate that the partition coefficients are pressure, temperature, and composition dependent. Therefore partitioning behavior over the appropriate range of pressure, temperature, and composition must be quantified, in order to model continuous extraction of melt during the adiabatic rise of mantle material. For this purpose, we have parameterized the partitioning behavior of the REE, Hf, Zr, U, and Th based on a simple thermodynamic model. Although these parameterizations cannot be used for retrieving thermodynamic constants yet, they do yield accurate descriptions of the partitioning behavior that are useful for modeling decompression melting. Our parameterizations show that the partitioning of trace elements is strongly dependent on the Ca and Al-content of the clinopyroxene (cpx) and REE are always incompatible in cpx on the peridotite solidus at pressures up to 3.4 GPa. For garnet the data indicate that the heavy REE partition coefficients decrease with increasing pressure. Our data also indicates that Pb is more incompatible than Ce in clinopyroxene; Ce and Pb have similar partition coefficients in garnet. Therefore the presence of a residual phase with high Pb partition coefficients is required to produce the near-constant Ce/Pb ratios in MORB and OIB. Sulfides are the most likely phase to buffer the Pb content in the melt. Except at small porosities (<0.3%), clinopyroxene on the peridotite solidus is unable to fractionate U from Th significantly (15% 230Th-excess), whereas garnet can fractionate U from Th effectively at porosities up to 1%. Therefore if the 230Th-excesses in mid-ocean ridge basalts are melting phenomena, then melting with garnet residual is required in order to be compatible with physical observations on porosities and upwelling rate at mid-ocean ridges. New model calculations that include the compositional dependent partitioning of the trace elements show that the predicted physical characteristics (depth and extent of melting, upwelling rate, porosity) of the MORB melting regime are similar for the Lu/Hf, Sm/Nd, and U-Th systems.