Card-based cryptography typically uses a physical deck comprising black and red cards to perform secure computations, where a one-bit value is encoded using a pair of cards with different colors such that the order of black to red represents 0 and red to black represents 1. One of the most fundamental classes of card-based protocols is the class of “card-minimal” n-input AND protocols, which require 2n face-down cards as input to securely evaluate the AND value after applying a number of shuffles; here, the 2n cards are minimally required to describe an n-bit input. The best n-input AND protocols currently known use two shuffles for n= 2, five shuffles for n= 3, and n+ 1 shuffles for n> 3. These upper bounds on the numbers of shuffles have not been improved for several years. In this work, we present a better upper bound for the n= 3 case by designing a new card-minimal three-input AND protocol using only two shuffles. Therefore, our proposed protocol reduces the number of required shuffles from five to two; we believe that this is a significant improvement.