The conditions of the solar wind that lead to a quiet magnetosphere are determined under the assumption that the quiet or baseline magnetosphere can be identified by prolonged periods of low values of the am index. We analyzed solar wind data from 1978 to 1984 (7 years) during periods in which am≤3 nT to identify those solar wind parameters that deviate significantly from average values. Parallel studies were also performed for prolonged periods of Kp=0, 0+ and AE<35 nT. We find that for quiet times the solar wind velocity (V), the interplanetary magnetic field magnitude (B), and the z component of the IMF (Bz) show distinctive variations from average values. We independently varied these solar wind parameters and the length of time the conditions must persist to minimize am. This was done with the additional requirement that our conditions yield a reasonable number of occurrences (5% of the data set). The resulting baseline conditions are V≤390 km/s; 180¿-arctan ‖ By/Bz ‖≤101¿, when Bz≤0 (no restriction on Bz positive); B≤6.5 nT; and persistence of these conditions for at least 5 hours. Minimizing the am index does not require a clear upper limit on the value of Bz as might be anticipated from the work of Gussenhoven (1988) and Berthelier (1980). Apparently, this is a result of the requirement that the conditions must occur 5% of the time. When the requirement is lowered to 1% occurrence, an upper limit to Bz emerges.