Active material for a positive electrode of a rechargeable alkaline electrochemical cell is made with nickel hydroxide particles or cobalt-coated nickel hydroxide particles treated with strongly oxidizing reagents such as alkali metal persulfate in alkaline solution. The active material also may be made with cobalt-coated nickel hydroxide particles having a high percentage of cobalt(III) on a surface or an average cobalt oxidation state of about 3 measured across the particles. The treated nickel hydroxide or cobalt-coated nickel hydroxide decreases the cobalt solubility in the alkaline electrolyte and increases the high-rate charge and discharge capability. The lower cobalt solubility decreases cobalt migration that can increase self discharge and lead to premature failure.