A programmable integrated circuit with lookup table circuitry is provided. The lookup table (LUT) circuitry may be formed using multiplexers. A multiplexer in the lookup table circuitry may be implemented using only tristate inverting circuits. Each tristate inverting circuit may include a first set of n-channel and p-channel transistors that receive a static control bit from a memory element and a second set of n-channel and p-channel transistors that receive true and complementary versions of a user signal. The first and second sets of transistors may be coupled in series between a positive power supply terminal and a ground power supply terminal. A LUT multiplexer implemented in this way need not include separate transmission gates at the output of each tristate inverting circuit and may exhibit minimal subthreshold leakage.