The mechanisms for forming bump structures reduce variation of standoffs between chips and package substrates. By planarizing the solder layer on bump structures on chips and/or substrates after plating, the heights of bump structures are controlled to minimize variation due to within die and within wafer locations, pattern density, die size, and process variation. As a result, the standoffs between chips and substrates are controlled to be more uniform. Consequently, underfill quality is improved.