Abstract: This invention is a beverage cup sleeve or holder that intended for the retail beverage industry. The invention's main objective is to contain the spills, drips, or condensation that occur when drinking coffee, tea, soda, or other beverages. This improved beverage cup sleeve or holder may take various forms during shipping and distribution; but, when installed, the improved beverage cup sleeve or holder provides a cuff to gather spills, drips, and/or condensation. In the case of the beverage cup holder, a retaining bottom provides for additional opportunities for absorption and containment. Both the sleeve (without retaining bottom) and holder (with bottom) designs should be made from an absorbent material and separate the beverage drinker from the drips, spills, and/or condensation.