In a sixth‐order solenoid of type I (or II), the field errors of second and fourth orders are compensated by a notch in the outer (or inner) cylindrical surface. The power efficiencyEF≡G/0.1792, where the Fabry factorGis defined in the same way as for an uncompensated cylindrical coil with the same least radius, and 0.1792 is the largest possible value ofGfor any such coil. The efficiency of a sixth‐order solenoid is defined to be ``near maximum'' whenEFhas a value no less than 98% of the maximum for any compensated coil of the same type and normalized volumeV. The 2% tolerance permits the choice of an experimental coil to be influenced by properties that may be more sensitive to changes in geometry than isEF. Coils of type I are relatively long, with a maximumEFof 0.692 atV≅200. In type II coils, the diameter often exceeds the length, and the maximumEFis 0.884 atV≅300. Separate tables withV1/2as argument list 100 solenoids of each type, with geometry, field strength,EF, and axial limits for field variations of 0.1% and 1.0%. All radial depths are so adjusted that the layer counts for the midplane and end sections are proportional to a pair of small integers. Though the 0.03% limits of a typical coil of type I could enclose the 1.0% limits of a type II coil of the same volume, the field error of the type II coil is less than 0.02% at the axial 1.0% limit of the same coil without the correcting notch.