This paper introduces the Extremum Consistency (EC) algorithm for avoiding local maxima and minima in a specialised domain. The most notable difference between this approach and others in the literature is that it places a greater importance on the width or consistency of an extremum than on its height or depth (amplitude). Short-term, high amplitude extrema can be encountered in many typical situations (such as noisy environments or due to hardware imprecision) and can cause problems with system accuracy. The EC algorithm is far less susceptible to these situations than hill climbing, convolution, thresholding etc., and tends to produce higher quality results. This paper describes the algorithm and presents results from practical experimentation, which illustrates its superiority over other forms of local extrema avoidance in three real-world applications.