A process for making phenol and/or cyclohexanone, the process comprising: (A) oxidizing a cyclohexylbenzene feed to obtain an oxidation product comprising cyclohexylbenzene, cyclohexylbenzene hydroperoxide and water; (B) removing at least a portion of the water from at least a portion of the oxidation product to obtain a cleavage feed; and (C) contacting at least a portion of the cyclohexylbenzene hydroperoxide in the cleavage feed with an acid catalyst in a cleavage reactor under cleavage conditions to obtain a cleavage product comprising phenol and cyclohexanone. The removing step may also comprises a step of removing a portion of the cyclohexylbenzene contained in the oxidation product. Water removal may be advantageously conducted in a water flashing drum before a cyclohexylbenzene hydroperoxide concentrator.