1. A method of encoding video data by a computing device, the method comprising: while concurrently performing either intra-prediction or inter-prediction with respect to one or more neighboring blocks of the video data that are adjacent to a current block: determining a first set of pre-defined intra-prediction modes for the current block of the video data to be encoded, wherein the first set of intra-prediction modes includes less intra-prediction modes than a total number of intra-prediction modes capable of being used to encode the current block; determining a second set of intra-prediction modes for the current block in addition to the first predefined set of intra-prediction modes, wherein the second set of intra-prediction modes is not pre-defined and includes a quantity of intra-prediction modes less than or equal to the total number of intra-prediction modes capable of being used to encode the current block, wherein both the first set and the second set collectively include less intra-prediction modes in total than the total number of intra-prediction modes capable of being used to encode the current block; computing an approximate cost that approximates a full rate distortion cost for each intra-prediction mode included in the first set of intra-prediction modes and each intra-prediction mode included in the second set of intra-prediction modes, wherein the approximate cost approximates a rate distortion cost of encoding the current block of video data using the corresponding one of the intra-prediction modes; storing, for performing intra-prediction using full rate distortion optimization, the approximate cost only for each intra-prediction mode identified in the first set of intra-prediction modes and for each intra-prediction mode identified in the second set of intra-prediction modes to a memory; and performing intra-prediction using full rate distortion optimization to encode the current block in accordance with one of the intra-prediction modes identified by the first set of intra-prediction modes or the second set of intra-prediction modes based on the approximate cost computed for each intra-prediction mode identified in the first set of intra-prediction modes and the second set of intra-prediction modes.