We have measured the thermoelectric power and resistivity of a series of Tl0.5+xPb0.5 - xSr2Ca1 - yYyCu2 O7 compounds in which the hole concentration can be varied to span the entire range from under-doped to over-doped, with Tc increasing from zero to a maximum and then decreasing to very low values. The thermopower changes from very large positive values in the under-doped region to small negative values in the over-doped region, with a small negative temperature derivative except in the extreme under-doped limit. We also report the thermopower of a series of under-doped YBa2 - xLaxCu4O8 compounds, which shows little temperature dependence but decreases in magnitude as x decreases. Our data support the decrease of the thermopower magnitude as the hole concentration in the CuO planes increases which was found in other systems. © 1992.