In this paper, we focus on the multiuser massive multiple-input single-output (MISO) downlink with low-cost 1-bit digital-to-analog converters (DACs) for PSK modulation, and propose a low-complexity refinement process that is applicable to any existing 1-bit precoding approaches based on the constructive interference (CI) formulation. With the decomposition of the signals along the detection thresholds, we first formulate a simple symbol-scaling method as the performance metric. The low-complexity refinement approach is subsequently introduced, where we aim to improve the introduced symbol-scaling performance metric by modifying the transmit signal on one antenna at a time. Numerical results validate the effectiveness of the proposed refinement method on existing approaches for massive MIMO with 1-bit DACs, and the performance improvements are most significant for the low-complexity quantized zero-forcing (ZF) method.