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We relax the usual assumption of Maxwellian velocity distributions in the interstellar medium (ISM) in the analysis of neutral He particle data from Ulysses and the Interstellar Boundary Explorer (IBEX). For Ulysses, the possibility that a narrow component from heavy neutrals is contaminating the He signal is considered, which could potentially explain the lower ISM temperature measured by Ulysses compared to IBEX. The expected heavy element contribution is about an order of magnitude too small to resolve that discrepancy. For IBEX, we find that modest asymmetries in the ISM velocity distribution can potentially improve the quality of fit to the first two years of data, and perhaps improve agreement with the Ulysses measurements.