A bill cap or baseball cap has a crown and a bill as conventional. Additional, the bill cap has an elastic panel affixed at an edge thereof to front and left side edges of the bill. The elastic panel is capable of being flipped between an upward position in which the panel extends upwardly from the bill, and a downward position in which the panel extends downwardly from the bill. In the downward position the panel provides additional shading for the eyes of the wearer and/or privacy for the wearer when viewed from the side, thus providing additional anonymity for the wearer such as from paparazzi.