This research presents three works all related by the subject of third-order distortion reduction in nonlinear circuits. Each one is a novel extension to previous work in that branch of electronics literature. All three follow the procedure of presenting a novel algebraic proof and following up with simulations and/or measurements to confirm the theoretical result. The works are generally themed around nonlinear low-frequency bipolar transistor circuits. Firstly, an investigation is conducted into a well documented effect in bipolar-junction transistors (BJTs) called inherent third-order distortion nulling. This effect is shown to be a fundamental result of the transistor’s transfer junction acting upon an input signal. The proof of a single BJT emitter-follower amplifier’s inherent null is examined which is well documented in the literature. This forms the basis for a novel extension in Darlington transistors where theory suggests the third-order null occurs at double the collector current of a single BJT. Discrete measurements of a CA3083 transistor array are undertaken and compared with theory and simulation data. These measurements confirm theory with reasonable accuracy. A temperature and process variation independent bias circuit is developed to solve one issue with using third-order distortion nulling. This work is interesting in that it branches into series resistance compensation for translinear circuits and stands as a useful circuit in its own right. Using stacks of matched forward-biased semiconductor junctions which conform to translinear conditions, a bias current can be generated which theoretically removes temperature and series resistance dependence on the particular BJT used. This proves useful for the previous work in distortion nulling, but also allows direct and accurate measurement of series resistance. Again, simulation and measurement data is obtained from discrete measurements of the proposed circuit, and the results conform with theory to a reasonable degree. Lastly, this work presents the analysis of a cascoded-compensation (Cascomp) amplifier. It presents the first fully nonlinear derivation of the Cascomp’s transfer function and its associated harmonic and intermodulation distortion components. The derivation reveals an interesting characteristic in which the third-order intermodulation distortion has multiple local minima. This characteristic has not yet been presented in the literature, and allows better optimisation of Cascomp amplifiers in any application. Again, this characteristic and its potential benefits are confirmed with simulation and discrete measurements. Observations of the presented works are discussed and built upon in the last chapter. This leads to suggestions on future research topics branching on from these works.