One of the biggest reasons to order Civil War pensions is the supporting documentation. To prove their service and family relationships, veterans included anything and everything, including the family Bible.
If you’re not sure you want the full pension file (which includes military paperwork) and your ancestor was from Bridgeport, check out Noble Pension database from the Connecticut State Library (http://www.cslib.org/noble.asp). A father and daughter team, the Noble family helped veterans apply for their pensions and kept copies of their supporting documentation. It’s a good way to see what your ancestor’s pension might hold.