The degree of control over plasma flow direction exerted by the compressed magnetic field in the dayside magnetosheath is examined by comparing ISEE 1 LEPEDEA data with hydrodynamic and magnetohydrodynamic predictions. Measured flow directions projected toward the subsolar region pass within ~1 RE of the aberrated theoretical hydrodynamic stagnation point in 11 of 20 cases analyzed. The remaining nine cases pass within ~2-3 RE of the stagnation point. One case with large deflection has been studied in detail with large-time-resolution plasma and magnetic field data both from ISEE 1 and from ISEE 3, in the role of a solar wind monitor. The deflected flow is persitent over a period of 1 1/2 hours, and its direction is consistent with a stagnation point displacement resulting from increased, asymmetric magnetic field pressure contributions during periods of low Alfven Mach number, as predicted by Russell et al. Of the other eight cases with large deflections, four are associated with flux transfer events identified independently by Berchem and Russell. The observed deflections in these cases are consistent with either the subsolar merging line or the antiparallel merging hypothesis, but not exclusively with one or the other. The results relating to the formation of a stagnation line rather than a stagnation point are inconclusive.