Adaptive HTTP streaming is the preferred method to deliver multimedia content in the internet. It provides multiple representations of the same content in different qualities (i.e. bit-rates and resolutions) and allows the client to request segments from the available representations in a dynamic, adaptive way depending on its context. The growing number of representations in adaptive HTTP streaming makes encoding of one video segment at different representations a challenging task in terms of encoding time-complexity. In this paper, information of both highest and lowest quality representations are used to limit Rate Distortion Optimization (RDO) for each Coding Unit Tree (CTU) in High Efficiency Video Coding. Our proposed method first encodes the highest quality representation and consequently uses it to encode the lowest quality representation. In particular, the block structure and the selected reference frame of both highest and lowest quality representations are then used to predict and shorten the RDO process of each CTU for intermediate quality representations. Our proposed method introduces a delay of two CTUs thanks to employing parallel processing techniques. Experimental results show significant reduction in time-complexity over the reference software 38% and the state-of-the-art 10% while quality degradation is negligible.