As technology scales down, the leakage energy accounts for more portion of total energy in a cache. Applying the Dynamic Voltage Scaling(DVS) to a cache, which is called a drowsy cache, is known as one of the most efficient techniques for reducing leakage energy in a cache. However, it increases the Soft Error Rate(SER) and many researchers began to doubt the reliability of a drowsy cache. In this paper, we show that the instruction cache(I-cache) can adopt the DVS without reliability problems for several reasons. First, an I-cache always stores read-only data, rarely incurring unrecoverable errors. In the I-cache, the soft error can be recovered by re-fetching from the lower level memory. Second, the effect of soft errors on performance is negligible, because the SEE is extremely low. Additional, considerable percentage of soft errors do not harm the performance. In this paper, the evaluation results show that the drowsy I-cache rarely increases unrecoverable errors and negligibly degrades the performance.