A series of K-phase solid solutions based on Cu substitutions by the first row transition metals Ti, V, Mn, Fe, Co, and Ni, and the IIB metal Zn, in the general composition La1.85Sr0.15Cu0.95M0.05O4-delta, were prepared by the conventional grinding and firing technique. The magnetization of the base composition La1.85Sr0.15CuO4-delta was observed to be paramagnetic at temperatures just above the superconducting transition temperature. At temperatures just below T(c), the superconducting diamagnetic magnetization was almost completely reversible, but considerable hysteresis associated with flux pinning was observed at 4.2 K. When V or Ni was substituted for Cu the magnetization at 4.2 K remained irreversibly diamagnetic, but the peak magnetization was reduced by 1.0-1.5 orders of magnitude, compared to the value observed for La1.85Sr0.15CuO4-delta. In samples containing Mn or Co, the magnetization at 4.2 K was essentially paramagnetic with the superposition of a small component of superconducting diamagnetic magnetization with a peak value 2 orders of magnitude smaller than the peak observed in the base composition. In samples containing Ti, Cr or Zn the superconducting diamagnetism at 4.2 K was almost completely suppressed, so that the peak diamagnetic magnetization was 3-4 orders of magnitude lower than the value observed in La1.85Sr0.15CuO4-delta while in the solid solution containing Fe the superconducting diamagnetic magnetization was completely suppressed.