The 2004 JPSM Practicum Survey was designed to evaluate the feasibility of conducting surveys with respondents via their cellular phones. The study is a dual-frame household sample, where 8,500 cell phone numbers and 4,688 landline numbers were selected. This paper addresses challenges faced in weighting the samples to produce approximately unbiased estimates of households with any type of telephone service. Because both frames include households with both landline and cellular telephone service, compositing the weights for the overlap is considered. Comparison of initial weighted estimates for the overlap population and comparisons to estimates from the February 2004 CPS supplement on telephone usage show those interviewed from the cell phone frame are more frequent cell phone users than those interviewed from the landline frame. This is consistent with findings from an earlier cell phone survey. We propose an approach to weighting designed to compensate for this bias and evaluate it by comparing estimates from this and other weighting schemes. Other features of the 2004 JPSM Practicum Survey, especially those related to response rates, are briefly reviewed.