Pillars having a directed compliance geometry are arranged to couple a semiconductor die to a substrate. The direction of maximum compliance of each pillar may be aligned with the direction of maximum stress caused by unequal thermal expansion and contraction of the semiconductor die and substrate. Pillars may be designed and constructed with various shapes having particular compliance characteristics and particular directions of maximum compliance. The shape and orientation of the pillars may be selected as a function of their location on a die to accommodate the direction and magnitude of stress at their location. A method includes fabricating pillars with particular shapes by patterning to increase surface of materials upon which the pillar is plated or deposited.