A method is provided for bonding a semiconductor chip to a packaging substrate while minimizing the variation in the solder ball heights and controlling the stress in the solder balls and the stress in the packaging substrate. During the solder reflow, the warp of the packaging substrate, including the absolute warp, thermal warp, and substrate to substrate variations of the warp, is constrained at a minimal level by providing a clamping constraint to the packaging substrate. During cool down of the solder balls, the stresses and strains of the solder joints are maintained at levels that do not cause tear of the solder joints or breakage of the packaging substrate by removing the clamping constraint. Thus, the bonding process provides both uniform solder height with minimized solder non-wets and stress minimization of the solder balls and the packaging substrate.