The solubilities of Platinum (Pt) and Rhodium (Rh) in a haplobasaltic melt (anorthite-diopside eutectic composition) have been determined experimentally by using the mechanically assisted equilibration technique at 1300°C, as a function of oxygen fugacity (10-12 < fO2 ≤ 1 bar), imposed by CO-CO2, N2-H2-H2O, Ar-O2, and air gas mixtures. Samples were analyzed by sample nebulization (SN) inductively coupled plasma-mass spectrometry and, using some of these samples as standards, also by laser ablation (LA) inductively coupled plasma-mass spectrometry. The latter is a true microanalytical technique that allows small-scale sample heterogeneity to be detected. At each oxygen fugacity step, a time-series of samples was taken, to demonstrate that the solubilities convergence on a constant value. In addition, solubilities were measured after both increasing and decreasing the imposed fO2. The results fall into three groups, according to oxygen fugacity. At high fO2s, (fO2 ≥ 10-2 bars), samples are homogenous at all sampling scales. Both Pt and Rh predominantly dissolve in the silicate melt as 2+ species, with some evidence for Pt4+ and Rh3+ at the highest fO2s studied (air and pure O2). From these data, we obtained the following expressions for the solubilities of Pt and Rh: Pt/ppb = 2100(fO2) + 10980(fO2)( 1/2 ) Rh/ppb = 68630(fO2)( 3/4 ) + 31460(fO2)( 1/2 ) At fO2 < 10-5 bars, the true solubilities of Pt and Rh appear to be obscured by Pt-Rh micronuggets, which remain suspended in the melt despite stirring on time scales of 103 h, resulting in samples that are heterogenous on the laser sampling scale. Samples at intermediate fO2 (10-2 to 10-5 bars) are affected by the micronugget problem on the sampling scale of the conventional SN-inductively coupled plasma mass spectrometry, but these can be filtered out by analyzing on the laser sampling scale.