This paper presents an analysis of a suggested method for improving fairness among competing adaptive HTTP video streams. The metrics used as fairness indicators are differences in achieved average rate and stability among the competing streams. The method analyzed is based on changing a fixed and equal video segment request rate of each stream, to either a per session unique or random request rate. The analysis is done by means of measurements in a controlled environment using the Microsoft Smooth Streaming solution. The findings are considered very positive as they show that it is possible to achieve a significant improvement in fairness by applying the suggested method. The main novelty of the paper is that it demonstrates the potential of achieving such improvements without modifying either client or server algorithms.