I have an offer on the table, and I want to work for the construction employer. However, the relocation package (COLA) isn't good enough. How do I negotiate for more?

As with most things related to job negotiation, you need the following two things. First, you need to have your homework done. Second, you need to know what you will walk away from and what you will accept. The former may help you determine the latter. If you can, go to the area where you'll be working. Gather data on cost of living. Create a comparison document that demonstrates that you understand the housing market, the cost of commuting, the coast of food, the differences in utilities. Take the cost comparisons to the construction employer and let them know where they are short and why. Sometimes, that's all it takes because they didn't understand what the differences really were. Sometimes, you'll simply learn what you will and won't accept. Either way, you will be doing yourself a favor in the long run. If you can't visit the area in which you'll be working, get on the internet and do the same research by finding real estate web sites from that area, by contacting utility companies, by examining commute maps, and by contacting grocery stores. It's all out there. Go and get it.