`BENpico` is a new and distinct variety of miniature rose plant primarily identified by its pure white flowers edged with dark red and its miniature hybrid tea flower form. Blooms are borne singly and in small clusters on long straight stems, good for cutting and ideal for exhibition. When in bloom the plant makes an outstanding, decorative perennial in the ground or in containers. Its semi glossy foliage offers good disease resistance in all areas of the Mainland United States.