I. forming a reaction mixture comprising a) a hydroxyl-containing starter, b) at least one alkylene oxide, c) a water insoluble polymerization catalyst complex that includes at least one double metal cyanide compound and d), as part of the water insoluble polymerization catalyst complex or as a separate component, at least one M⁵ metal or semi-metal compound, in which the M⁵ metal or semi-metal is selected from aluminum, magnesium, manganese, scandium, molybdenum, cobalt, tungsten, iron, vanadium, tin, titanium, silicon and zinc, and is bonded to at least one alkoxide, aryloxy, carboxylate, acyl, pyrophosphate, phosphate, thiophosphate, dithiophosphate, phosphate ester, thiophosphate ester, amide, oxide, siloxide, hydride, carbamate, halide or hydrocarbon anion, and

II. polymerizing the alkylene oxide onto the hydroxyl-containing starter in the presence of the water insoluble polymerization catalyst complex and the M⁵ metal or semi-metal compound to produce the polyether,

wherein the water insoluble polymerization catalyst complex contains 0.5 to 2 weight percent potassium, based on the weight of the water insoluble polymerization catalyst complex, the water insoluble polymerization catalyst being prepared by a method comprising forming a starting solution containing zinc compound and a potassium cyanometallate compound in a solvent that includes water and a liquid aliphatic alcohol, and reacting the zinc compound and cyanometallate compound in the presence of the M5 metal compound to produce the double metal cyanide catalyst, which precipitates from solution, and washing the precipitated catalyst zero or one time with water and/or a liquid aliphatic alcohol.