In massively multithreaded architectures, redundantly executing the same instruction with the same operands in different threads is a significant source of inefficiency. This paper introduces Dimensionality-Aware Redundant SIMT Instruction Elimination (DARSIE), a non-speculative instruction skipping mechanism to reduce redundant operations in GPUs. DARSIE uses static markings from the compiler and information obtained at kernel launch time to skip redundant instructions before they are fetched, keeping them out of the pipeline. DARSIE exploits a new observation that there is significant redundancy across warp instructions in multi-dimensional threadblocks. For minimal area cost, DARSIE eliminates conditionally redundant instructions without any programmer intervention. On increasingly important 2D GPU applications, DARSIE reduces the number of instructions fetched and executed by 23% over contemporary GPUs. Not fetching these instructions results in a geometric mean of 30% performance improvement, while decreasing the energy consumed by 25%.