New three-level designs for fitting second-order response surfaces are obtained by three methods. New designs for 9, 10, and 13 factors are obtained by combining two-level factorial designs and incomplete block designs. New designs for 6, 8 and 10 factors are obtained by design rotation; these designs are rotations of central composite designs. Two sequences of design (for 7, 11 and 15 factors) are obtained by using a Hadamard matrix to reduce v+1 linearly dependent variables to a design for v factors. One of these sequences of design corresponds to a rotation of uniform shell designs; the other sequence is complementary to the rotated uniform shell designs in the sense that the O's and + or - 1's of the design points are interchanged.