Which of the following is a common use for the slow-speed handpiece?

The slow-speed handpiece is primarily used for procedures that require more control and gentler handling, making it ideal for polishing amalgam restorations. This application is crucial because polishing requires a steady hand and precision to ensure the surface of the restoration is smooth and shiny without removing excess material.

In contrast, cutting teeth generally requires a high-speed handpiece, which is designed for faster and more aggressive cutting actions. Removing large amounts of decay also typically involves high-speed equipment to efficiently and effectively take out the affected tissue. Accelerated cleansing is more suited for high-speed handpieces as well, as they allow for rapid removal of debris and improve the efficiency of cleansing procedures. Therefore, polishing amalgam restorations is the most fitting application for a slow-speed handpiece due to the specific control and gentleness it offers.