We present a double-subtraction observing technique which was used in an attempt to detect the Sunyaev-Zeldovich effect in the radio lobes of 0742 + 318, 1721 + 343, 2221 - 02, and 2349 + 32. The observations were made with the NRAO 12 m telescope at 3 mm. The 3-sigma upper limits of the observations are used to place upper limits on the radio lobe thermal pressure which supposedly confines the jet in each observed radio source. The thermal pressure upper limits are compared with minimum pressure measurements from combined array VLA maps at 6 cm. In all cases, the upper limit on the radio lobe pressure determined from the Sunyaev-Zeldovich effect exceeds the jet minimum pressure; therefore, these observations do not require magnetic pressure to confine the jets. Using the pressure limits, the adiabatic shock condition, and an estimate of the intergalactic medium pressure, we set upper limits on the jet Mach number relative to the intergalactic medium. A detailed analysis of the telescope data indicated no significant systematic offsets.